Explain the mistake that is made.
Find the exact value of
$$
\tan \left(-\frac{7 \pi}{6}\right)
$$
The tangent function is an even function.
$$
\tan \left(\frac{7 \pi}{6}\right)
$$
$$
\text { Write } \frac{7 \pi}{6} \text { as a sum. }
$$
$$
\tan \left(\pi+\frac{\pi}{6}\right)
$$
$$
\begin{aligned}
&\text { Use the tangent sum identity, }\\
&\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}
\end{aligned}
$$
$$
\frac{\tan \pi+\tan \left(\frac{\pi}{6}\right)}{1-\tan \pi \tan \left(\frac{\pi}{6}\right)}
$$
Evaluate the tangent functions on the right.
$$
\begin{array}{c}
0+\frac{1}{\sqrt{3}} \\
\hline 1-0 \\
\frac{\sqrt{3}}{3}
\end{array}
$$
Simplify.
This is incorrect. What mistake was made?