Those numbers are quite big

Calculus Level 4

limx0ln(tan(π4+432394829x))sin3427954283x\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 ab\dfrac{a}{b} for coprime positive integers a,ba,b, find a+ba+b.

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