The doctrine of the Trinity is quite simply the only way to make sense of the story, and that in two different ways.
On the one hand, the doctrine is the only way to make sense of the Biblical story, the gospel story. When Jesus talks to his Father, and promises his followers that he will send the Spirit from the Father, and when he says that seeing him is seeing the Father, or that the presence of the Spirit is his own presence... How can we make sense of that without the Trinity?
On the other hand, the doctrine is the only way to make sense of my personal story as a Christian, my everyday story. When I pray, I speak to the Father in Jesus' name - and at the same time, I am aware that I would not, left to myself, pray at all; it is only the presence of Another within me that motivates and empowers me... How can I make sense of myself without the Trinity?
The doctrine of the Trinity is just the only way of describing the actor(s) in this drama which makes sense of what they actually do.