1. Solve the equation

   $$\arctan (\alpha )+\arctan (3)=\frac{\pi }{4}$$

2. Express

   $$\arctan (2)-\arctan \left(\frac{1}{2}\right)$$

   as a single $\arctan .$

3. Find a general expression for

   $$\arctan (\alpha )+\arctan (\beta )$$

   as a single $\arctan .$

Start by taking $\tan$ of both sides of the equation. Recall that, since $\tan$ and $\arctan$ are inverse functions, we have

for any $x.$

Let $y=\arctan (2)-\arctan \left(\frac{1}{2}\right)$ and then take $\tan$ of both sides.