Answer
$$1$$
Work Step by Step
$$\eqalign{
& \int_0^{\pi /4} {se{c^2}\theta } d\theta \cr
& {\text{find antiderivative use integration formulas from table 4}}{\text{.2}}{\text{.1}} \cr
& \int_0^{\pi /4} {se{c^2}\theta } d\theta = \left( {\tan \theta } \right)_0^{\pi /4} \cr
& {\text{part 1 of fundamental theorem of calculus}} \cr
& = \tan \left( {\frac{\pi }{4}} \right) - \tan \left( 0 \right) \cr
& {\text{recall that tan}}\left( {\frac{\pi }{4}} \right) = 1{\text{ and tan}}\left( 0 \right) = 0 \cr
& = 1 - 0 \cr
& = 1 \cr
& {\text{then}} \cr
& \int_0^{\pi /4} {se{c^2}\theta } d\theta = 1 \cr} $$