The claim that God is one in essence, but three in Person, is the traditional brief statement of the doctrine of the Trinity. But it is insufficient. An additional principle is necessary in order to sustain this doctrine's meaning: the principle of equality.
The Persons share equally in the divine nature. If this were not the case, then one would be superior to the others, and since the Supreme Being is God alone, the Trinity immediately reduces to a Unitarian or Monistic view.
Then the principle of diversity would be lost -- because how could there be diversity with only One eternal principle? And likewise the principle of unity would become meaningless; how can we speak of a unity among one thing?
Therefore, all three principles: unity, diversity, and equality, stand or fall together. The doctrine of the Trinity solves many problems in philosophy as well as in understanding the Word of God. To reject any of these principles would throw theology back to the ancient pagan beliefs of polytheism, pantheism, and monism.