Modern Unitarians don’t believe in anything and are essentially agnostics seeking the same kind of fellowship routinely experienced by truly Christian congregations. If they say they are Christian, they mean they kind of like Jesus. I’m sorry, but it is true, as anyone with any exposure to that “denomination” will confirm. . So I believe this person was baiting you.
Tell him that the Trinity is a mystery, which is true. We’re not supposed to understand it. Too bad if that does not satisfy him.
(BTW unfortunately Unitarians are the custodians of numerous important church resources in the US, including the Old Ship Church in Hingham, Massachusetts, the oldest worship building in the US, All Saints (ha) Unitarian in Washington, one of the most impressive churches there, and many others, some of which have magnificent organs that are these days only used to play nature worship music).