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Note 19 - Government Grants (Details Textual) - USD ($) $ in Thousands	12 Months Ended
	Jun. 30, 2025	Jun. 30, 2024
Government Assistance, Income, Increase (Decrease)	$ 145	$ 113
Financial Assistance Received From the Singapore Government [Member]
Government Assistance, Income, Increase (Decrease)	82	23
Financial Assistance Received From the United States Government [Member]
Government Assistance, Income, Increase (Decrease)	48	57
Financial Assistance Received From the Chinese Government [Member
Government Assistance, Income, Increase (Decrease)	$ 15	$ 33

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

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

X

- Details

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

X

- Details

Name:	us-gaap_GovernmentAssistanceTypeAxis=trt_FinancialAssistanceReceivedFromTheUnitedStatesGovernmentMember
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: