If π/3∫π/4(sin3θ−cos3θ−cos2θ)(sinθ+cosθ+cos2θ)2010(sinθ – InterviewSolution

1.	If π/3∫π/4(sin3θ−cos3θ−cos2θ)(sinθ+cosθ+cos2θ)2010(sinθ)2012(cosθ)2012 dθ=(a+√b)n−(1+√c)nd where a,b,c and d are all positive integers, then the value of a+b+c+d is
Answer» If $π / 3 \int π / 4 \frac{({sin}^{3} θ - {cos}^{3} θ - {cos}^{2} θ) (sin θ + cos θ + {cos}^{2} θ)^{2010}}{(sin θ)^{2012} (cos θ)^{2012}} d θ = \frac{(a + \sqrt{b})^{n} - (1 + \sqrt{c})^{n}}{d}$ where $a, b, c$ and $d$ are all positive integers, then the value of $a + b + c + d$ is

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