Which one of the following is one of the solutions of the equation of the equation $$\tan 2\theta \cdot \tan \theta = 1\,?$$

Solution :
$$\eqalign{ & \tan 2\theta \cdot \tan \theta = 1 \cr & \Rightarrow \frac{{2\tan \theta }}{{1 - {{\tan }^2}\theta }} \cdot \tan \theta = 1 \cr & \Rightarrow 2\,{\tan ^2}\theta = 1 - {\tan ^2}\theta \cr & \Rightarrow 3\,{\tan ^2}\theta = 1 \cr & \Rightarrow {\tan ^2}\theta = \frac{1}{3} = {\left( {\frac{1}{{\sqrt 3 }}} \right)^2} \cr & \Rightarrow {\tan ^2}\theta = {\tan ^2}\left( {{{30}^ \circ }} \right){\tan ^2}\left( {\frac{\pi }{6}} \right)\left[ {\because \theta = n\pi \pm \frac{\pi }{6}} \right]; \cr & \therefore \theta = \frac{\pi }{6} \cr} $$