Certainly none of the "nontrinitarian positions" mentioned in the Wiki article:
not Binitarianism (one deity/two persons) [though the position of some is very similar to this one]:
"There are
three living
persons of the heavenly trio; in the name of these
three great powers --the Father, the Son, and the Holy Spirit--those who receive Christ by living faith are baptized." {Ev 615.1}
"The prince of the power of evil can only be held in check by the power of God in the
third person of the Godhead, the Holy Spirit." {Ev 617.2}
not Unitarianism (one deity/one person): (see quotes above)
not the Oneness belief (there is one God, a
singular spirit who manifests himself in many different ways, including as Father, Son and Holy Spirit): (see quotes above)
not modalism (God is one person who has revealed himself in three forms or modes; God does not exist as Father, Son and Holy Spirit at the same time): (see quotes above)
not the Church of Jesus Christ of Latter-day Saints' view of the Godhead as three separate beings who are one in purpose rather than essence:
"The words of Christ were full of deep meaning as he put forth the claim that he and the Father
were of one substance, possessing the same attributes." {ST, November 27, 1893 par. 5}
So our view would be closer to the "standard" view.
The Athanasian Creed says:
That we worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons; nor dividing the Essence. For there is one Person of the Father; another of the Son; and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one; the Glory equal, the Majesty coeternal. Such as the Father is; such is the Son; and such is the Holy Ghost. The Father uncreated; the Son uncreated; and the Holy Ghost uncreated. The Father unlimited; the Son unlimited; and the Holy Ghost unlimited. The Father eternal; the Son eternal; and the Holy Ghost eternal. And yet they are not three eternals; but one eternal. As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite. So likewise the Father is Almighty; the Son Almighty; and the Holy Ghost Almighty. And yet they are not three Almighties; but one Almighty. So the Father is God; the Son is God; and the Holy Ghost is God. And yet they are not three Gods; but one God. So likewise the Father is Lord; the Son Lord; and the Holy Ghost Lord. And yet not three Lords; but one Lord. For like as we are compelled by the Christian verity; to acknowledge every Person by himself to be God and Lord; So are we forbidden by the Catholic Religion; to say, There are three Gods, or three Lords. The Father is made of none; neither created, nor begotten. The Son is of the Father alone; not made, nor created; but begotten. The Holy Ghost is of the Father and of the Son; neither made, nor created, nor begotten; but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. And in this Trinity none is before, or after another; none is greater, or less than another. But the whole three Persons are coeternal, and coequal. So that in all things, as aforesaid; the Unity in Trinity, and the Trinity in Unity, is to be worshipped. He therefore that will be saved, let him thus think of the Trinity.
I see apparently nothing wrong with this Creed. We believe in three divine persons in one substance (essence), and these persons are coeternal and coequal. Ellen White uses the term "coequal" for the persons of the Godhead:
"It was to save the transgressor from ruin that he who was co-equal with God, offered up his life on Calvary." {RH, June 28, 1892 par. 3}