I have stumbled across something beautiful! I haven’t the time to write of it now, but I can allude to it without fear. Eventually, I will reproduce a very fascinating formula for \pi.

But first:

Consider the following expression:

cos \dfrac{\xi}{2} cos \dfrac{\xi}{4} cos \dfrac{\xi}{8} ... cos \dfrac{\xi}{2^n}

It can be simplified into a very simple quotient of sin in terms of \xi.