Evaluate the $\tan (\arctan 3 + \arctan 4)$.

Let $A = \arctan 3$, then $\tan A = 3$
Let $B = \arctan 4$, then $\tan B = 4$
 

$\begin{align}
\tan (\arctan 3 + \arctan 4) & = \tan (A + B) \\
\\
& = \dfrac{\tan A + \tan B}{1 - \tan A \cdot \tan B} \\
\\
& = \dfrac{3 + 4}{1 - 3 \cdot 4}\\
\\
& = -\dfrac{7}{11}
\end{align}$

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