Trick Magic Item lets you activate items from other traditions on its own.
You don't need Unified Theory for this. The explicit outcome of using Trick Magic Item is that you can use things like scrolls and wands from other magical traditions.
Suppose Willhelm the Wizard wants to use a scroll to cast Soothe, an occult spell. If they have Trick Magic Item, they can attempt an occultism check to activate the item. Unified Theory isn't necessary here.
Combining with Unified Theory
If you want to combine it with Unified Theory for other reasons, can you? As an example, let's go back to Willhelm the Wizard trying to cast Soothe. This time they have both Trick Magic Item and Unified Theory.
Willhelm tries to use the scroll, but can't activate because they aren't an occult spellcaster. So they decide to use Trick Magic Item. They can now attempt an occultism check to activate the scroll.
As they are using an action (and skill feat!) to make an occultism check as determined by the magical tradition of the scroll, they make invoke Unified Theory. Now Willhelm instead makes an Arcana check to activate the scroll. Since they must be at least legendary in Arcana to take Unified Theory, this is probably a pretty sweet deal.