Prove the identity

$\displaystyle -\sin \frac{\pi}{7} + \sin \frac{2\pi}{7} + \sin \frac{3\pi}{7} + \sin \frac{4\pi}{7}+\sin \frac{5\pi}{7} - \sin \frac{6\pi}{7} = \sqrt{7}$

P.S. If I find a question interesting, is there a way to save the thread to look at it later (ex. using "favorite" or "private watch list"). Is there such facility in this forum? I couldn't find any means of saving a question that I like... (Crying)