My fourth integration problem

Calculus Level 4

\[ \displaystyle \int_{0}^{{1} / {2} } \frac{dx}{\sqrt{9-36x^{2}-\arcsin^{2}(2x) +4x^{2} \arcsin^{2} (2x)}} \]

If the integral above is equal to \( \displaystyle \dfrac{a}{b} \arcsin \left( \dfrac{\arcsin(c)}{d}\right) \), where \(a,b,c\) and \(d\) are positive integers, with \(a, b\) are coprime, find \(a+b+c+d\).

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