Question 8
Find the positive integer $n$ such that $$
\begin{aligned} &\arctan\frac{1}{3} + \arctan\frac{1}{4} \\ &\quad {}+ \arctan\frac{1}{5} + \arctan\frac{1}{n} = \frac{\pi}{4}. \end{aligned}
$$
\begin{aligned} &\arctan\frac{1}{3} + \arctan\frac{1}{4} \\ &\quad {}+ \arctan\frac{1}{5} + \arctan\frac{1}{n} = \frac{\pi}{4}. \end{aligned}
$$