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Note 21 - Leases (Details Textual) - USD ($) $ in Thousands	3 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Nov. 01, 2025	Jun. 30, 2025
Lessor Asset under Operating Lease, Term (Year)	20 years
Depreciation, Lessor Asset under Operating Lease	$ 17	$ 17
Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year	473
Lessee, Operating Lease, Liability, to be Paid, Year One	297			$ 560
Lessee, Operating Lease, Liability, to be Paid, Year Two	$ 277			$ 146
Subsequent Event [Member] | Lease Agreements Beginning November 1, 2025 [Member]
Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year			$ 44
Lessee, Operating Lease, Liability, to be Paid, Year One			66
Lessee, Operating Lease, Liability, to be Paid, Year Two			66
Lessee, Operating Lease Liability, Payments Due, After Year Two			$ 161
Minimum [Member]
Lessor, Operating Lease, Term of Contract (Month)	12 months
Lessee, Operating Lease, Remaining Lease Term (Year)	1 year
Maximum [Member]
Lessor, Operating Lease, Term of Contract (Month)	48 years
Lessee, Operating Lease, Remaining Lease Term (Year)	5 years

X

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid after the second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

No definition available.

+ Details

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Namespace Prefix:	trt_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Represents term for lessor asset under operating lease.

+ References

No definition available.

+ Details

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Namespace Prefix:	trt_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 235
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477314/942-235-S99-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-4

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-6

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 235
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477314/942-235-S99-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-4

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-6

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease having initial or remaining lease term in excess of one year to be paid in remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-6

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Remaining lease term of operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-7A

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Term of lessor's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479773/842-30-50-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Amount of depreciation expense for lessor's underlying asset for which right to use has been conveyed to lessee under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479773/842-30-50-13

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482099/360-10-50-1

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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- Details

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- Details

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