Evaluate `int(sin^(3)(theta//2)d theta)/(cos theta//2 sqrt(cos^(3)theta+cos^(2)theta + cos theta))`.

Evaluate: intsin^3(theta/2)/(cos(theta/2)sqrt(cos^3theta+cos^2theta+costheta))d theta

Evaluate int((2 sin theta + sin 2 theta)d theta)/((cos theta-1)sqrt(cos theta + cos^(2) theta + cos^(3) theta)) .

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

cos theta+sqrt(3)sin theta=2

cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

Solve cos theta+cos 2theta+cos 3theta=0 .

(sin5theta+sin2theta-sin theta)/(cos5theta+2cos3theta+2cos^(2)theta+costheta) is equal to

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta

int (d ( cos theta))/(sqrt(1-cos^(2) theta))

The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^(4)theta cos^(2)theta+cos^(6)theta sin^(2)theta+3sin^(2)thetacos^(4)theta is equal to