Answer
$$ x=15 ^{\circ} , \ 105^{\circ},\ 195^{\circ},\ 285^{\circ} $$
Work Step by Step
Given $$ \tan2x= \frac{\sqrt{3} }{3}$$
From the figure, we find the intersection points between $y= \tan2x$ and $ y=\frac{\sqrt{3} }{3}$; we get
$$ x=15 ^{\circ} , \ 105^{\circ},\ 195^{\circ},\ 285^{\circ} $$
