Note 21 - Leases (Details Textual) - USD ($) $ in Thousands	6 Months Ended
Mar. 31, 2025	Mar. 31, 2024
Lessor Asset under Operating Lease, Term (Year)	20 years
Depreciation, Lessor Asset under Operating Lease	$ 17	$ 34
Operating Lease, Lease Not yet Commenced [Member]
Unrecorded Unconditional Purchase Obligation, to be Paid, Remainder of Fiscal Year	5
Unrecorded Unconditional Purchase Obligation, to be Paid, Year One	62
Unrecorded Unconditional Purchase Obligation, to be Paid, Year Two	62
Unrecorded Unconditional Purchase Obligation Due After Two Years	$ 123
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

Represents term for lessor asset under operating lease.

No definition available.

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

- Definition

Amount of fixed and determinable portion of unrecorded unconditional purchase obligation to be paid after 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). Includes, but is not limited to, lease not yet commenced.

+ References

No definition available.

+ Details

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

- 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

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

- 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

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

- 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

Name:	us-gaap_OperatingLeasesIncomeStatementDepreciationExpenseOnPropertySubjectToOrHeldForLease
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of fixed and determinable portion of unrecorded unconditional purchase obligation 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). Includes, but is not limited to, lease not yet commenced.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 440
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482648/440-10-50-4

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

+ Details

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

- Definition

Amount of fixed and determinable portion of unrecorded unconditional purchase obligation 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). Includes, but is not limited to, lease not yet commenced.

+ References

+ Details

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

- Definition

Amount of fixed and determinable portion of unrecorded unconditional purchase obligation to be paid in remainder of current fiscal year.

+ References

No definition available.

+ Details

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

- Details

Name:	us-gaap_UnrecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=us-gaap_OperatingLeaseLeaseNotYetCommencedMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: