# Calculust - 3

Calculus Level 5

$\large \int^{\pi /3}_{\pi /4} \dfrac{(\sin^3\theta-\cos^2\theta-\cos^3\theta)(\sin\theta+\cos\theta+\cos^2\theta )^{2007}}{(\sin\theta)^{2009}(\cos\theta)^{2009}} \,d\theta$

If the above integral is of the form $\dfrac{(a+\sqrt{b})^n-(1+\sqrt{c})^n}{d},$

where $$a,b,c$$ and $$d$$ are positive integers, find $$a+b+c+d$$.

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