Answer
$1$
Work Step by Step
$$\eqalign{
& \int_0^{\pi /3} {\sec \theta \tan \theta } d\theta \cr
& {\text{Recall that }}\frac{d}{{dx}}\left[ {\sec x} \right] = \sec x\tan x,\,{\text{ then}} \cr
& \int_0^{\pi /3} {\sec \theta \tan \theta } d\theta = \left[ {\sec \theta } \right]_0^{\pi /3} \cr
& {\text{Use The Fundamental Theorem of Calculus}},{\text{ Part 2}} \cr
& \left[ {\sec \theta } \right]_0^{\pi /3} = \sec \left( {\frac{\pi }{3}} \right) - \sec \left( 0 \right) \cr
& {\text{Simplify}} \cr
& \left[ {\sec \theta } \right]_0^{\pi /3} = 2 - 1 \cr
& \left[ {\sec \theta } \right]_0^{\pi /3} = 1 \cr} $$
