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If int(pi/4)^(pi/3) ((sin^3theta-cos^3th...

If `int_(pi/4)^(pi/3) ((sin^3theta-cos^3theta-cos^2theta)(sintheta+costheta+cos^2theta)^2007)/((sintheta)^2009( costheta)^2009))d theta`=`((a+sqrtb)^n-(1+sqrtc)^n)/d` where a,b,c,d are all positive integers. Find the value of (a+b+c+d).

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