Thread: Prove the following beautiful identity of the square root of 7.

1. Prove the following beautiful identity of the square root of 7.

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...

2. Still working on the identity (nice one!), but

Originally Posted by mathwizard
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...
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