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

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

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

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