I am having difficulty performing the following summation. I think there might be simple sum, but i am unable to see how to get there. Any help would be much appreciated.
$$\sum_{m=1}^{N-1} \frac{sin\left(\frac{\pi m}{N}\right)sin\left(\frac{\pi n m}{N}\right)}{sin^2\left(\frac{\pi m}{2N}\right)}$$
Note that n and N are positive integers.
Many thanks Lee