Note 15 - Other Income (Details Textual) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021
Government Grant	$ 62	$ 152	$ 160	$ 412
Other Nonoperating Income (Expense) [Member]
Government Grant	$ 0
Government Grant, Foreign, COVID-19 Relief Income		$ 107	$ 61	$ 350

Represents grant received from a foreign government.

No definition available.

Name:	trt_GovernmentGrantForeignCovid19ReliefIncome
Namespace Prefix:	trt_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration