Chapter 5.6, Problem 73ES

Evaluate each limit by interpreting it as a Riemann sum in which the given interval is divided into $n$ subintervals of equal width.

$\underset{n\to +\infty }{\lim }{\displaystyle \underset{k=1}{\overset{n}{\sum }}\frac{\pi }{4n}{\sec }^2\left(\frac{\pi k}{4n}\right)};\left[0,\frac{\pi }{4}\right]$