# 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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