Hi !

(I know a proof, so it's like a challenge question)

Prove that $\displaystyle \sin \tfrac \pi m \cdot \sin \tfrac{2 \pi}{m} \cdots \sin \tfrac{(m-1) \pi}{m}=\tfrac{m}{2^{m-1}}$, where $\displaystyle m \in \mathbb{N}$ and $\displaystyle m \geqslant 2$