I came across the formula (24) in the WolframMathWorld article on Web page http://mathworld.wolfram.com/TrigonometryAngles.html where no source of the proof could be identified by me.
The formula is $$\prod_{k=1}^{\lfloor \frac n2\rfloor}\sin(\frac{k\pi}{n})=\sqrt{\frac{n}{2^{n-1}}}$$
I am near a proof but it is rather intricate and maybe awkward and much to complicated.
Does anybody know the source of the original proof or is there an elementary homework-style one without deeper necessary experience ?
