Those numbers are quite big

Calculus Level 4

\[\large \displaystyle \lim_{x \rightarrow 0} \dfrac {\ln (\tan (\frac{\pi}{4} + 432394829x))}{\sin {3427954283x}}\]

If the value of the limit above can be represented as \(\dfrac{a}{b}\) for coprime positive integers \(a,b\), find \(a+b\).

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