First: I would never say that the phrase: "god is three persons in one, each with a simultaneous independent and non-independent existence" is "correct". I would say that, based on my own subjective experience, in keeping with my epistemological view, that is what I believe.
I think that this is as far as a believer can go when talking about their faith.
I guess I just need to ask this then:
Do you believe that god exists outside of your mind?
Yes, but that's more like my belief that I love my wife, or that everything happens for a reason, it isn't verifiable in the way that scientific claims are verifiable.