$\cos x.tan3x = 0\left( {x \ne \dfrac{\pi }{6} + \dfrac{{k\pi }}{3},k \in \mathbb{Z}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
\tan 3x = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \\
x = \dfrac{{k\pi }}{3}
\end{array} \right.,k \in \mathbb{Z}$