Hey just to make sure im correct i came up with
x= 2pi/3 and x=5pi/3
are these all the solutions.....
$\displaystyle \tan x + \sqrt{3} = 0$
$\displaystyle \tan x = - \sqrt{3}$
$\displaystyle x = \tan ^{-1} (- \sqrt{3})$
$\displaystyle \frac{2\pi}{3}, \frac{5 \pi}{3}$
You can have infinite solution. If the range is between $\displaystyle 0 \ge x \ge 2\pi$ then you are correct.