ln\ln and ln2\ln^2

Calculus Level 4

If given that limx0ln(2cos2x)ln2(sin3x+1)=ab,\displaystyle \lim_{x \to 0} \dfrac{\ln(2-\cos2x)}{\ln^2(\sin3x + 1)} = \dfrac{a}{b} ,

find a2+b2a^2 + b^2 where aa and bb are relatively prime,

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