All true Christians believe in the doctrine of the trinity. But not all true Christians reflect on a deeper understanding of the trinity. Still worse, others believe it is not even relevant to do so. If God found it worthy to reveal the mystery of the trinity to us, then there must be implications for how we are to live. We lose a richness of the Faith when we hold to this reductionistic view. God has revealed Himself through the universe and through us. We are made in His image and likeness. We can look for concrete images of the trinity in our daily life.
The mystery of the trinity is indeed a mystery and actually, the greatest mystery. All the more reason to delve into its mysteries. The universe is a mystery to us, and yet only the absurd would argue that scientific discoveries are irrelevant. Humans are mysteries, too. But strangely enough, we try to figure them out, too! And this "figuring" is how we show love. This is how we can be a "gift" to the other. If I am allergic to seafood, and my boyfriend makes me a salmon dinner for our anniversary I would feel completely unloved and say, "Don't you know me at all!? Don't you love me?!" Of course, the mystery of the human person can never be fully realized but that doesn't merit not partaking in the discovery.
If this is how I relate to people, then this must be a clue as to how God wishes me to relate to Him and to love Him. To ask, "Who are you God? What is this trinity that You are?" If I believe that God is trinity, then I must reflect into that mystery of the Triune God if I'm going to reflect about Him at all. I can't just reflect on God, or Son (Jesus), or Holy Spirit without reflecting on all three since it is their particular relationship with one another that distinguishes them in person.
More on the Trinity to follow...