\[ \large \int_0^{\pi/2} ( \ln (\cos x))^2 ( (\ln(\cos x))^2 - 6x^2) \, dx \]

If the integral above is equal to \( \dfrac{\pi^a}2 (\ln 2)^b - \dfrac{\pi^c}d \), where \(a,b,c\) and \(d\) are positive integers, find \(a+b+c+d\).

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