Answer
$1$
Work Step by Step
$\tan{(A+B)} = \dfrac{\tan{A}+\tan{B}}{1- \tan{A} \tan{B}}$
$2= \dfrac{\tan{A}+\dfrac{1}{3}}{1- \dfrac{1}{3} \tan{A}}$
$2-\dfrac{2}{3}\tan{A} = \tan{A} + \dfrac{1}{3}$
$\dfrac{5}{3} = \dfrac{5}{3} \tan{A}$
$\tan{A} = 1$
