If you were making up a theology from scratch, you would never opt to include a notion as allusive and difficult to explicate as the Trinity. It is an idea that has forced itself upon faithful believers simply because no viable alternative conclusions satisfy the available data.
This gives rise to the somewhat reluctant realisation that we are seeking to describe something far beyond our everyday experience of life. We simply have neither the words, nor even the concepts, to do justice to the divine realities presented to us.
Every now and then, in moments of relational clarity, we might glimpse something of the depth of interconnectivity that bonds the three distinct persons of the Trinity. But for the most part, this aspect of our God remains mysterious to us.
Never-the-less, it is worth exploring - or at the very least acknowledging it is so.