Limit Revision

Calculus Level 3

$\displaystyle\lim_{x \rightarrow 0} \left( \dfrac{1}{\sin^2x} - \dfrac{1}{x^2}\right)$

If the limit above is equal to $\dfrac ab$ , where $a$ and $b$ are coprime positive integers, find the value of $a+b$ .

Submit your answer as 0 if you don't think the limit exist.