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