Find the value of the sum $$\arctan\left(\dfrac{1}{2}\right)+\arctan\left(\dfrac{1}{3}\right)$$
We were also given a hint of using the trigonometric identity of $\tan(x + y)$
Hint
$$\tan\left(x+y\right)\:=\:\dfrac{\tan x\:+\tan y}{1-\left(\tan x\right)\left(\tan y\right)}$$

Let $x = \arctan \dfrac{1}{2}$ and $y = \arctan \dfrac{1}{3}$. Then, $\tan x = \dfrac{1}{2}$ and $\tan y = \dfrac{1}{3}$. 
Using that formula, you can easily compute $\tan(x+y)$. Do you see how to get $x+y$ from that?
