$\sin {10}^0+\sin 20+\sin {30}^0+\dots \dots \sin {360}^0=$

$$\begin{gathered} \sin {10}^0+\sin {20}^0+.......+\sin {30}^0 \\ \mathrm{A}-\mathrm{B}={180}^0 \Rightarrow \sin \mathrm{A}+\sin \mathrm{B}=0 \\ \sin {10}^0+\sin {190}^0+\sin {20}^0+\sin {200}^0+...... \\ +\sin {170}^0+\sin {350}^0+\sin {180}^0+\sin {360}^0 \\ =0 \end{gathered}$$