\(\sin \left( {2x - \frac{\pi }{3}} \right) = - \frac{{\sqrt 3 }}{2}\)

\( \Leftrightarrow \sin \left( {2x - \frac{\pi }{3}} \right) = \sin \left( { - \frac{\pi }{3}} \right)\)

\( \Leftrightarrow \left[ \begin{array}{l}2x - \frac{\pi }{3} = - \frac{\pi }{3} + k2\pi \\2x - \frac{\pi }{3} = \pi - \left( { - \frac{\pi }{3}} \right) + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}2x = - \frac{\pi }{3} + \frac{\pi }{3} + k2\pi \\2x = \pi + \frac{\pi }{3} + \frac{\pi }{3} + k2\pi \end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}2x = k2\pi \\2x = \frac{{5\pi }}{3} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = k\pi \\x = \frac{{5\pi }}{6} + k\pi \end{array} \right.\left( {k \in \mathbb{Z}} \right)\).

Vậy phương trình đã cho có các nghiệm là \(x = k\pi \) và \(x = \frac{{5\pi }}{6} + k\pi \) với k ∈ ℤ.