Times ago, I used to think about some trigonometric equalities. Now, I have faced a new one with different one:
Show that if $z^7+1=0$ then cos$(\frac{\pi}{7})$+cos$(\frac{3\pi}{7})$+cos$(\frac{5\pi}{7})=\frac{1}{2}$ wherein $z\in\mathbb C$.
Thanks