\(\ln\) and \(\ln^2\)

Calculus Level 3

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

find \(a^2 + b^2 \) where \(a\) and \(b\) are relatively prime,

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