Answer
$2+\sqrt3$
Work Step by Step
I would evaluate $\tan 75^\circ$ by the formula for $\tan(a+b)$ where $a=30^\circ,b=45^\circ$. Then just follow the formula and evaluate the known values. These are: $\tan75^\circ=\frac{\tan30^\circ+\tan45^\circ}{1-\tan30^\circ\tan45^\circ}=\frac{\frac{1}{\sqrt3}+1}{1-\frac{1}{\sqrt3}1}=2+\sqrt3$
