I need to evaluate the product $\displaystyle \prod_{m=n-a}^{n-1} \sin \left( \pi m /n \right)$.

I've found this identity: $\displaystyle \prod_{m=1}^{n-1} \sin \left( \pi m /n \right) \equiv \frac{n}{2^{n-1}}$, which looks useful but isn't quite what I need.

Does anyone know of a generalisation of this identity so that the lower range is $\displaystyle n-a$?