$\begin{array}{l} y = \sin \left( {2x - \dfrac{\pi }{3}} \right)\cos \left( {2x + \dfrac{\pi }{3}} \right) = \dfrac{1}{2}\left[ {\sin 4x - \sin \left( {\dfrac{{2\pi }}{3}} \right)} \right]\\ = \dfrac{1}{2}\sin 4x - \dfrac{{\sqrt 3 }}{4}\\ - 1 \le \sin 4x \le 1 \Rightarrow \dfrac{{ - 2 - \sqrt 3 }}{4} \le y \le \dfrac{{2 - \sqrt 3 }}{4}\\ \Rightarrow \left\{ \begin{array}{l} \max y = \dfrac{{2 - \sqrt 3 }}{4}\\ \min y = \dfrac{{ - 2 - \sqrt 3 }}{4} \end{array} \right.\\ \end{array}$
