If $A>0, B>0$ and $Α + B = \frac{\pi}{6} ,$ then the minimum value of $\tan A + \tan B$ is :

Question

$\begin{array}{1 1} (1)\; \sqrt 3 - \sqrt 2 \\ (2)\; 2 - \sqrt 3 \\ (3)\; 4 - 2\sqrt 3 \\ (4)\; \frac{2}{\sqrt 3} \end{array}$