$E= sin(\frac{\pi}{5})+sin(\frac{2\pi}{5})+ sin(\frac{3\pi}{5})+ sin(\frac{4\pi}{5})+ sin\pi+ sin(\pi+ \frac{\pi}{5})+ sin(\pi+\frac{2\pi}{5})+ sin(\pi+\frac{3\pi}{5})+ sin(\pi+\frac{9\pi}{5})$
Do $sin(\pi+\alpha)= -sin\alpha$
$\Rightarrow E= sin\pi= 0$