Prove that : `4 sin theta sin (theta + pi/3) sin (theta + (2pi)/3) = sin 3 theta`

Prove that sin theta cos^(3)theta - cos theta sin^(3) theta = (1)/(4) sin 4 theta .

Prove that 4sin theta sin((pi)/(3)+theta)sin((2 pi)/(3)+theta)=sin3 theta

Prove that all values of theta: |(sintheta, costheta, sin2theta),(sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin (2theta+(4pi)/3)),(sin (theta- (2pi)/3), cos (theta- (2pi)/3), sin (2theta- (4pi)/3))|=0

The value of the determinant |sin theta,cos theta,sin2 thetasin(theta+(2 pi)/(3)),cos(theta+(2 pi)/(3)),sin(2 theta+(4 pi)/(3))sin(theta-(2 pi)/(3)),cos(theta-(2 pi)/(3)),sin(2 theta-(4 pi)/(3))

If f( theta ) = sin ^(3)theta + sin ^(3)( theta + (2pi)/(3)) + sin ^(3)( theta + (4pi)/(3)) then the value of f((pi)/(18)) + f((7pi)/(18)) is ___________.

Prove that sin(theta-(pi)/(6))+cos(theta-(pi)/(3))=sqrt(3)sin theta

Prove that :(sin theta+2sin3 theta+sin5 theta)/(sin3 theta+2sin5 theta+sin7 theta)=(sin3 theta)/(sin5 theta)

Prove that sin^(2)theta

Prove that sin theta sin(60^(@)-theta) sin(60^(@)+theta)=1/4 sin3theta .