Determine which of the following regions has an area equal to the given limit without evaluating the limit: $$\underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}} \frac{\pi}{4n}\tan\left(\frac{i\pi}{4n}\right)$$

A. The area of the region under the graph of $y=\sec(x)$ on the interval $[0,\pi/8].$
B. The area of the region under the graph of $y=\tan(x)$ on the interval $[0,\pi/8].$
C. The area of the region under the graph of $y=\sec(x)$ on the interval $[0,\pi/4].$
D. The area of the region under the graph of $y=\tan(x)$ on the interval $[0,\pi/4].$