trigonometry - If $alpha=frac{2pi}{7}$,prove that $sinalpha+sin2alpha+sin4alpha=frac{sqrt7}{2}$

If $\alpha=\frac{2\pi}{7}$,prove that $\sin\alpha+\sin2\alpha+\sin4\alpha=\frac{\sqrt7}{2}$

We need to find $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$

$=\sin\frac{2\pi}{7}+\sin\frac{3\pi}{7}-\sin\frac{\pi}{7}$