Compute $\sum_{j=1}^k\cos^n(j\pi/k)\sin(nj\pi/k)$

Compute $\sum_{j=1}^k\cos^n(j\pi/k)\sin(nj\pi/k)$

Compute the series
$\sum_{j=1}^k\cos^n(j\pi/k)\sin(nj\pi/k)$
Hint: the answer is in fact 0