Evaluate the $\tan (\arctan 3 - \arctan 2)$.

Let $A = \arctan 3$ then $\tan A = 3$.
Let $B = \arctan 2$ then $\tan B = 2$.
 

$\begin{align} \tan (\arctan 3 - \arctan 2) & = \tan (A - B) \\ \\ & = \dfrac{\tan A - \tan B}{1 + \tan A \cdot \tan B} \\ \\ & = \dfrac{3 - 2}{1 + 3 \cdot 2}\\ \\ & = \dfrac{1}{7} \end{align}$

Use your calculator. Set it in RAD mode.