Evaluate the double integral

Calculus Level 5

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

Evaluate the double integral above. If the answer comes in the form of \(a\pi (b-\ln c)\), where \(\gcd (a,b,c)=1\), then find \(a+b+c\).

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