Apologetics Timeout

Whenever I debate the legitimacy of Sola Scriptura with a Protestant friend, I always like to bring up the Trinity, and how most Protestants accept it despite the fact that the word does not appear in the Bible. The usual response I get to this is "yeah, but Scripture supports it." While this is true, the problem that my Protestant friends fail to see is that the Bible does not itself provide a definition to "Trinity". When taken out of the Christian context, Trinity simply means three separate things or objects; there is no suggestion that while these three things (i.e., persons) are distinct, they nevertheless subsist in one essence (i.e., God). Indeed, attaching such a definition to Trinity is logically incoherent. Why, then, do most Protestants call the Trinity "the Trinity"? As much as they may deny it, Protestants are more reliant on the authority of the Catholic Church than they think.