Solving trigonometric equations help

Hey guys.

Here's the problem. We did not cover a problem like this in class on Thursday, so that's why I'm confused.

$\displaystyle 3\tan^22x-1=0$

I began to solve the trigonometric equation, and here's how I went about it.

$\displaystyle 3\tan^22x = 1$

$\displaystyle tan^22x = \frac{1}{3}$

Here's where I'm stuck. I'm thinking of taking the square root of both sides, but then I'm left with:

$\displaystyle \tan2x = \pm\frac{\sqrt{3}}{3}$

And then once I divide two out, I'm left with a weird fraction that doesn't look like anything that can be found on the unit circle.

Am I doing anything wrong here?