$\begin{array}{l}
\sin \left( {x - \dfrac{\pi }{3}} \right) - \dfrac{{\sqrt 2 }}{2} = 0\\
\Leftrightarrow \sin \left( {x - \dfrac{\pi }{3}} \right) = \dfrac{{\sqrt 2 }}{2}\\
\Leftrightarrow \sin \left( {x - \dfrac{\pi }{3}} \right) = \sin \dfrac{\pi }{4}\\
\Leftrightarrow \left[ \begin{array}{l}
x - \dfrac{\pi }{3} = \dfrac{\pi }{4} + k2\pi \\
x - \dfrac{\pi }{3} = \dfrac{{3\pi }}{4} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{7\pi }}{{12}} + k2\pi \\
x = \dfrac{{13\pi }}{{12}} + k2\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$
