Polar Coordinates and Complex Numbers · Superchallenge problem

Evaluate $\displaystyle\sum_{k=0}^{10}\binom{10}{k}\cos(60k)^\circ$, that is, $\binom{10}{0}\cos0^\circ+\binom{10}{1}\cos60^\circ+\binom{10}{2}\cos120^\circ+\cdots+\binom{10}{10}\cos600^\circ$.