Proving $\cos\frac{9}{11}\pi + \cos\frac{7}{11}\pi + \cos\frac{5}{11}\pi + \cos\frac{3}{11}\pi + \cos\frac{1}{11}\pi = \frac{1}{2}$

Question

Why is:

$$\cos\frac{9}{11}\pi + \cos\frac{7}{11}\pi + \cos\frac{5}{11}\pi + \cos\frac{3}{11}\pi + \cos\frac{1}{11}\pi = \frac{1}{2}$$