#### Answer

$2+\sqrt{3}$

#### Work Step by Step

Use the subtraction formula for tangent, $\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$.
$\tan\left(-\frac{7\pi}{12}\right)$
$=\tan\left(-\frac{\pi}{4}-\frac{\pi}{3}\right)$
$=\frac{\tan(-\frac{\pi}{4})-\tan\frac{\pi}{3}}{1+\tan(-\frac{\pi}{4})\tan\frac{\pi}{3}}$
$=\frac{-1-\sqrt{3}}{1+(-1)*\sqrt{3}}$
$=\frac{-1-\sqrt{3}}{1-\sqrt{3}}$
$=\frac{-1-\sqrt{3}}{1-\sqrt{3}}*\frac{1+\sqrt{3}}{1+\sqrt{3}}$
$=\frac{-1-2\sqrt{3}-3}{1-3}$
$=\frac{-4-2\sqrt{3}}{-2}$
$=2+\sqrt{3}$