$\begin{array}{l}
\cos \left( {4x - \dfrac{\pi }{3}} \right) = 1\\
\Leftrightarrow \cos \left( {4x - \dfrac{\pi }{3}} \right) = \cos 0\\
\Leftrightarrow 4x - \dfrac{\pi }{3} = k2\pi \\
\Leftrightarrow x = \dfrac{\pi }{{12}} + \dfrac{{k\pi }}{2}\left( {k \in Z} \right)
\end{array}$