Tính $E = \sin \dfrac{\pi }{5} + \sin \dfrac{{2\pi }}{5} + ... + \sin \dfrac{{9\pi }}{5}$.

$\begin{array}{l}E = \sin \dfrac{\pi }{5} + \sin \dfrac{{2\pi }}{5} + ... + \sin \dfrac{{9\pi }}{5}\\ = \left( {\sin \dfrac{\pi }{5} + \sin \dfrac{{9\pi }}{5}} \right) + \left( {\sin \dfrac{{2\pi }}{5} + \sin \dfrac{{8\pi }}{5}} \right) + ...\\ + \left( {\sin \dfrac{{4\pi }}{5} + \sin \dfrac{{6\pi }}{5}} \right) + \sin \dfrac{{5\pi }}{5}\\ = \left[ {\sin \dfrac{\pi }{5} + \sin \left( {2\pi  - \dfrac{\pi }{5}} \right)} \right] + \left[ {\sin \dfrac{{2\pi }}{5} + \sin \left( {2\pi  - \dfrac{{2\pi }}{5}} \right)} \right]\\ + ... + \left[ {\sin \dfrac{{4\pi }}{5} + \sin \left( {2\pi  - \dfrac{{4\pi }}{5}} \right)} \right] + \sin \pi \\ = \left[ {\sin \dfrac{\pi }{5} + \sin \left( { - \dfrac{\pi }{5}} \right)} \right] + \left[ {\sin \dfrac{{2\pi }}{5} + \sin \left( { - \dfrac{{2\pi }}{5}} \right)} \right]\\+ ... + \left[ {\sin \dfrac{{4\pi }}{5} + \sin \left( { - \dfrac{{4\pi }}{5}} \right)} \right] + 0\\ = \left( {\sin \dfrac{\pi }{5} - \sin \dfrac{\pi }{5}} \right) + \left( {\sin \dfrac{{2\pi }}{5} - \sin \dfrac{{2\pi }}{5}} \right) + ...\\ + \left( {\sin \dfrac{{4\pi }}{5} - \sin \dfrac{{4\pi }}{5}} \right)\\ = 0 + 0 + ... + 0 = 0\end{array}$