Limit as $x$ approaches $0$ with constant $a$ Find the limit where $a$ is a constant
$$ \lim_{x \to  0}\frac{\left [ \cos(a+x)-\cos(a-x) \right ]^2}{\tan^2(3x)} $$
I don't know what to do. At first I thought I could replace $a$ with an arbitrary number and then solve the limit but then I got stuck as to how to use the squeeze theorem on this question. Any help?

Hint: $$ \frac{\left[ \cos(a+x)-\cos(a-x) \right]^2}{\tan^2(3x)} = \frac{4\sin^2 a \sin^2 x}{\tan^2(3x)} = \frac{4\sin^2 a }{9}\frac{(3x)^2}{\tan^2(3x)} \frac{\sin^2 x}{x^2}.$$
