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 \(a+b\).