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Note 16 - Government Grants (Details Textual) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 31, 2025	Mar. 31, 2024	Mar. 31, 2025	Mar. 31, 2024
Government Assistance, Income, Increase (Decrease)	$ 22	$ 12	$ 93	$ 89
Financial Assistance Received From the Singapore Government [Member]
Government Assistance, Income, Increase (Decrease)	19	7	81	19
Financial Assistance Received From the Chinese Government [Member
Government Assistance, Income, Increase (Decrease)	$ 3	$ 5	$ 12	12
Employee Retention Credit [Member]
Government Assistance, Income, Increase (Decrease)				$ 57

X

- Definition

Amount of increase (decrease) in income from government assistance.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 832
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483507/832-10-50-3

+ Details

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

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_GovernmentAssistanceTypeAxis=trt_FinancialAssistanceReceivedFromTheChineseGovernmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_GovernmentAssistanceTypeAxis=trt_EmployeeRetentionCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: