# Integral 2

Calculus Level 3

$\large \int_{0}^{\pi/2}\frac{d\theta}{{(\cos^3{\theta}+\sin^3{\theta})}^{2/3}} = \frac{a\pi^2/b}{\Gamma^3{(c/d)}}$

The equation above holds true for positive integers $$a$$, $$b$$, $$c$$, and $$d$$, where $$\gcd(a,b)=\gcd(c,d)= 1$$ and $$c$$ is minimized. Find $$1000a+100b+10c+d$$.

Notation: $$\Gamma (\cdot)$$ denotes the gamma function.

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