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 $latex \pi$.

But first:

Consider the following expression:

$latex \cos \dfrac{\xi}{2} \cos \dfrac{\xi}{4} \cos \dfrac{\xi}{8} … \cos \dfrac{\xi}{2^n}$

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