Definite integral of sec x from 0 to pi over 6

Compute $\displaystyle\int_0^{\pi/6}\sec x\,dx$.

$\tfrac12\ln3\approx0.549$. An antiderivative is $\ln|\sec x+\tan x|$. At $\pi/6$ this is $\ln\!\left(\tfrac{2}{\sqrt3}+\tfrac{1}{\sqrt3}\right)=\ln\sqrt3$, and at $0$ it is $\ln1=0$.