Limit

Calculus Level 4

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

Given that $a$ and $b$ are positive integers where $\gcd (a,b)=1$ , find the value of $a+b$ .