Answer
$$\sqrt 3 $$
Work Step by Step
$$\eqalign{
& \int_0^{\pi /3} {{{\sec }^2}\theta } d\theta \cr
& {\text{We know that }}\frac{d}{{dx}}\left[ {\tan x} \right] = {\sec ^2}x\cr
&{\text{ Then}}{\text{,}} \cr
& \int_0^{\pi /3} {{{\sec }^2}\theta } d\theta = \left( {\tan \theta } \right)_0^{\pi /3} \cr
& {\text{Evaluate}} \cr
& = \tan \left( {\frac{\pi }{3}} \right) - \tan \left( 0 \right) \cr
& {\text{Simplify}} \cr
& = \sqrt 3 - 0 \cr
& = \sqrt 3 \cr} $$
