Answer
$\frac{6\sqrt3}{\pi}$
Work Step by Step
The general formula for average rate of change from $x$ to $y$ is $\frac{f(y)-f(x)}{y-x}.$
Hence here:
$\frac{\tan{(2\cdot \frac{\pi}{6})}-\tan{(2\cdot0)}}{\frac{\pi}{6}-0}
\\=\frac{\tan{\frac{\pi}{3}}-\tan{0}}{\frac{\pi}{6}}
\\=\frac{\sqrt3-0}{\frac{\pi}{6}}
\\=\frac{6\sqrt3}{\pi}$
