Oh, and almost forgot this. Trinity is shorthand as far as I'm concerned for Father God, Jesus and the Holy Spirit. It is not a necessary term as the essentials of it are in the Bible and stand on their own. I'd just as soon reference the three of them than use the word unless I were writing it all out, which is the only time I bother with it. So, in short, it is not in the Bible, nor does it need to be. I'm not certain I really understand the point behind someone coming up with the term to be quite honest - I don't see that it is needed. The early Christians understood the different natures of God without a buzz word in the 1st century and I did in this century.
Well it is a specific term. It means Three people in one God. It doesn't mean a Triumvirate which would suggest three gods, and it doesn't mean three parts of one whole god put together, it means Three Persons Who are One God.
Tertullian
"Thus the connection of the Father in the Son, and of the Son in the Paraclete, produces three coherent Persons, who are yet distinct One from Another. These Three are, one essence, not one Person, as it is said, 'I and my Father are One' [John 10:30], in respect of unity of Being not singularity of number" (ibid., 25).
It was hard for some people to understand, and if you live when paganism was still strong you would understand why we needed a specific word to describe it. You will find that most (all, as far as I know) unusual beliefs of the Church, not expressly found in the Bible (none are contradictory to it, though I know you disagree) are really an explanation of some truth to counter a challenge to it.