\[\begin{array}{l}
\;Sin{\rm{ }}\left( {{\rm{ }}3x + {\rm{ }}\frac{{2\pi }}{3}} \right){\rm{ }} - {\rm{ }}Sin{\rm{ }}\left( {{\rm{ }}x{\rm{ }} - {\rm{ }}\frac{{7\pi }}{5}} \right){\rm{ }} = {\rm{ }}0\\
\Leftrightarrow Sin{\rm{ }}\left( {{\rm{ }}3x + {\rm{ }}\frac{{2\pi }}{3}} \right) = Sin{\rm{ }}\left( {{\rm{ }}x{\rm{ }} - {\rm{ }}\frac{{7\pi }}{5}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
3x + \frac{{2\pi }}{3} = x - \frac{{7\pi }}{5} + k2\pi \\
3x + \frac{{2\pi }}{3} = \pi - x + \frac{{7\pi }}{5} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \frac{{ - 31\pi }}{{15}} + k2\pi \\
4x = \frac{{ - 11\pi }}{{10}} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{ - 31\pi }}{{30}} + k\pi \\
x = \frac{{ - 11\pi }}{{40}} + \frac{{k\pi }}{2}
\end{array} \right.\left( {k \in Z} \right)\\
vay:S = \{ \frac{{ - 31\pi }}{{30}} + k\pi ;x = \frac{{ - 11\pi }}{{40}} + \frac{{k\pi }}{2}\}
\end{array}\]