$\begin{array}{l}
\Leftrightarrow 3{\tan ^2}\left( {3x + \dfrac{\pi }{6}} \right) = 1\\
\Leftrightarrow {\tan ^2}\left( {3x + \dfrac{\pi }{6}} \right) = \dfrac{1}{3}\\
\Leftrightarrow \left[ \begin{array}{l}
\tan \left( {3x + \dfrac{\pi }{6}} \right) = \dfrac{{\sqrt 3 }}{3}\\
\tan \left( {3x + \dfrac{\pi }{6}} \right) = - \dfrac{{\sqrt 3 }}{3}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
3x + \dfrac{\pi }{6} = \dfrac{\pi }{6} + k\pi \\
3x + \dfrac{\pi }{6} = - \dfrac{\pi }{6} + k\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{k\pi }}{3}\\
x = - \dfrac{\pi }{9} + \dfrac{{k\pi }}{3}
\end{array} \right.\left( {k \in \mathbb{Z}} \right)
\end{array}$
