how to prove $\prod_{k=1}^{p-1} \sin(\frac{\pi k}{p}) = \frac{p}{2^{p-1}}$? i found this relation whilst trying to evaluate the norm (over $\mathbb{Q}$) of $1-\zeta$ for $\zeta$ a primitive $p$-th root of unity ($p$ supposed prime)
$$
\prod_{k=1}^{p-1} \sin(\frac{\pi k}{p}) = \frac{p}{2^{p-1}}
$$
as yet i have no means of proving it. any suggestions?

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*Kindly see this article page number $5$.

