Double Integral

Calculus Level 5

\[\large \int_{0}^{1} \int_{0}^{1} \frac{ \arcsin( \sqrt{1-x} \sqrt{y})}{\sqrt{1-x} \sqrt{xy-y+1} \sqrt{y} } \; dx \; dy \]

Evaluate the double integral above. If the answer comes in the form of \(-\dfrac{a}{b} \zeta(3) + \dfrac{c}{d} \pi^2 \ln 2\), where \(\gcd (a,b)=1\) and \(\gcd (c,d)=1\), then find \(a+b+c+d\).

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