Ever since I first became a Christian in 1981, I've always found the strained "explanations" for the trinity to be interesting and, frankly, sometimes comical. There is the egg, water, etc. The way I see it is much simpler. God is one. And the father, the Son, and the holy spirit are all God. They are one. But he details are much harder for us to understand than quantum mechanics or how a multiverse actually would exist.
The “explanations” you cite tend to be heretical, due to modalism or the dividing of God into parts. It is sufficient to say that the Trinity is one God in three persons, the Father, Son and Holy Ghost, who are co-equal, and proceed from the Creed.
That is, it becomes a source of arguments between believers.
All Christians believe in the Trinity and the Incarnation. Really, this is the definitive way of separating the wheat from the chaff, so to speak. The J/Ws, Swedenborgian New Church people, Moonies, Mormons, Christian Science, non-Trinitarian Adventists and Oneness Pentecostals, among others, all reject the Trinity. Even Islam was initially an anti-Trinitarian heresy, until Muhammed shifted focus away from converting Arabian Jews and Christians and towards converting the Pagans of Mecca, which he symbolized one morning in Medina by initially leading prayer facing Jerusalem as per the Jewish custom that he had followed, before changing to face Mecca. Nonetheless, Islam was classified as a heretical form of Christianity for several centuries, by such thought leaders of the early church as the extremely pious and learned monk St. John of Damascus, from the celebrated Mar Saba monastery in the Holy Land (which along with St. Catharine’s Monastery in Sinai, St. Anthony’s Monastery and the Syrian Monastery in Egypt and other related Coptic monasteries such as those in Scetis, the convent in the Aramaic speaking town of Maaloula which was occupied by Al Qaeda, the Syriac Orthodox monasteries in Tur Abdin, and the Greek Monasteries on Mount Athos and on the Island of Patmos and the Meteora valley, are the most important surviving Christian monasteries in the Eastern Mediterranean area.
Whereas all normal Christian churches that are generally recognized by other churches as Trinitarian accept it, and baptize people in the name of the Father, Son and Holy Ghost based on Matthew 28:19, and also accept and teach the doctrine of the Incarnation as found in Luke 1-2, Matthew 1-2, and John 1:1-18.
So if anyone, while believing in the doctrine referred to by the word Trinity, which is a prerequisite to being a Christian, argues with me about the name, I will dismiss that argument as at best quibbling over a nominal value, and more seriously, as offensive to the millions of Christians who since the time of the early Church have died at the hands of non-Trinitarian heretics who have persecuted us, such as Arians and Muslims.
Also you know the Nicene Creed is part of the Christian Forum Statement of Faith, so one never needs to worry about having to argue with a non-Trinitarian here. Likewise the Statement of Faith also bans denying the Apostolate of St. Paul and also separately the site rules ban arguing for the KJV only position, which was implemented shortly after I joined, and I think the mods did that simply because the KJV only people would not leave us alone and were utterly impossible to reason with, with some even going so far as to insist that ancient Greek manuscripts be discarded in favor of translations from the KJV owing to its status as an inspired revelation, which is of course ludicrous. Now, don’t get me wrong, I love the elegant Jacobean English prose of the King James Version as much as anyone possibly could, but those people were unbearable regardless of whether one liked the KJV or didn’t like the KJV.