Here is a statement of the doctrine of the Trinity in a nutshell that I developed in that comments section:
There is one divine life (ousia / essence) that is structured or characterized by three-fold communion (persones / hypostases). There is one will / locus of consciousness / personhood, with three forms or modes of being / activity. These forms are radically perichoretic, which means that the divinity of each is equal to that of the whole. The three forms are distinguished only by the unique combinations of their mutual relationships. One God existing eternally in the communion of his three-fold life.