More fundamentally, sure, I’ll grant you that perhaps the Trinity isn’t completely, baldly nonsensical; but what reason do we have for supposing that it is at all true?
Well, it's hard to suppose it's true at all if you don't already believe that a man called Jesus of Nazareth was simultaneously God and the Son of God (Abrahamic). 
That's not meant to be flippant or anything, btw.
Indeed, the Trinity is based in the revelation of the Bible. While St. Augustine tries to argue for why it would be necessary for God to be triune, it's not a conclusion one would come to in absence of the words of Christ positing a strange and paradoxical relationship between Him and the Heavenly Father.
