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

Prove that sintheta+sin(theta+(2pi)/(3))+sin(theta+(4pi)/(3))=0

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

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))

|(sin theta, cos theta, 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)))|=

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

If sin^(3)theta+sin^(3)(theta+(2pi)/(3))+sin^(3)(theta+(4pi)/(3))=a sinb theta . Find the value of |(b)/(a)| .

If sin^(3)theta+sin^(3)(theta+(2pi)/(3))+sin^(3)(theta+(4pi)/(3))=a sinb theta . Find the value of |(b)/(a)| .

Prove that for 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 |(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))|

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