I'm working through some trig questions and don't understand this one:

$\displaystyle \lim_{ x \to 0} \frac{1 - \cos 2x}{3x^{2}}$

My first thought was since $\displaystyle \lim_{x \to 0} \cos x = 1$, the answer would be 0, but alas, it turned out to be $\displaystyle \frac{2}{3}$

Could anyone shed some light on this?