The Teaching that only One God exists and no other
It doesn't say that. That's a different idea. Jews and Muslims believe in one God as well but not the trinity. Same with Unitarians.
The trinity is a later invention. You still can't explain what difference it makes. How would the world look if there was just one God, not trinity? How would it look if there was no God at all? How is it more likely than the Net of Indra?
If it was then Jews would believe in it. It isn't and they don't. The Trinity is an invention by some Christians. All Christians don't accept it and the ones that do still disagree with each other about all sorts of other things. So the Trinity doesn't really make any difference. It doesn't solve any problems, doesn't add any knowledge.