Well, I'll chip in my thoughts.
The word 'Trinity' is not 'Biblical'. The word used in the NT is translated 'Godhead'. A previous poster has already said this.
The NT writers clearly believed (as do I) that the Father is God, the Son, Jesus Christ is God and the Holy Spirit is God. They also believed that God is one God.
Then they went on to state various stuff about Father, Son and Holy Spirit, even at some points saying that One did the same as another One.
They didn't try - at any time - to define 'Godhead' (certainly not by the word 'Trinity'). They just spoke about it/Him (the Godhead word is not personal but a label although God is so I use both pronouns so you can use your preference).
Then came along the early Church fathers who found that this wasn't a very good state of affairs and began formulating theology and theory - instead of just accepting what the early Church believed. They then coined the translated word 'Trinity'.
And that's where it went very pear-shaped. It really would be much easier if we just talked about the Godhead and accepted what the NT says about it/Him without trying to go *too much* further.
"Godhead" is an English word, and the Bible is written in Greek. Therefore, Godhead is not a biblical word either.
If you want to be precise, use the word
theotēs. If you insist upon precision, then be fully precise. I know that KJV people insist on the word Godhead but the apostles didn't use King Jimmy..it didn't drop out of Jesus' sleeve as he ascended.
The word Trinity or Triune is a word used to confine a concept, so it is not wrong in itself. For example, we don't find the word Bible in the Bible either, but we know it's a "collection of 66 books that comprise the Old and New Testament canon". The Bible doesn't use the word Millennium either, but we know it refers to the "1000 year reign of Jesus Christ". If I held a similar position regarding those concepts, I'd simply use the phrases in quotes instead of the short descriptive word of Bible and Millennium. That would get tiring though.
Words which describe concepts are not wrong, else we need to revamp much of our vocabulary.
Rapture is another such word. The word actually comes from the Latin translation of the Greek word
harpagisometha. Yet, we use the word Rapture in order to describe this concept, and not many people have problems with that.
Godhead is just an old English word. I personally don't like to use it and use Triune or Trinity. Also, it sounds nasty to me so I don't like to use it in reference to God. Triunity might be a better word but Trinity suits me fine. I don't cater to KJVers or cultists.