In this page http://mathworld.wolfram.com/TrigonometryAnglesPi13.html
I found equation (11) and (12).
$$\cos^2\frac{\pi}{13}+\cos^2\frac{3\pi}{13}+\cos^2\frac{4\pi}{13}=\frac{11+\sqrt{13}}{8}$$
$$\sin\frac{\pi}{13}+\sin\frac{3\pi}{13}+\sin\frac{4\pi}{13}=\sqrt{\frac{13+3\sqrt{13}}{8}}$$
How to prove it ?
Thanks in advances