I was able to simplify this expression using transformation formulae. The answer turned out to be
$$\frac{\sqrt{7}}{2}=\sin\left(\frac{2\pi}{7}\right)+\sin\left(\frac{4\pi}{7}\right)+ \sin\left(\frac{8\pi}{7}\right)$$
How could this be simplified using complex numbers(assume that I now know little to nothing about transformation formulae but only the complex definition of sines and cosines)
