" 6."sin alpha+sin(alpha+theta)+sin(alpha+2 theta)=0

Find the general value of theta from the equation sinalpha+sin(alpha+theta)+sin(alpha+2theta)=0 .

Find the general value of theta from the equation sinalpha+sin(alpha+theta)+sin(alpha+2theta)=0 .

If sintheta sin(2alpha+theta)sin(4alpha + theta)...sin(2(n-1)alpha+theta)=(sinntheta)/(2^(n-1)) where 2nalpha=pi then cot(theta)+cot(2alpha+theta)+cot(4alpha+theta)+.......+cot(2n-1)alpha+theta)=

sin(3 theta+alpha)+sin(3 theta-alpha)+sin(alpha-theta)-sin(alpha+theta)=cos alpha

sin(3theta+alpha)+sin(3theta-alpha)+sin(alpha-theta)-sin(alpha+theta)=cosalpha

sin(3theta+alpha)+sin(3theta-alpha)+sin(alpha-theta)-sin(alpha+theta)=cosalpha

sin(3theta+alpha)+sin(3theta-alpha)+sin(alpha-theta)-sin(alpha+theta)=cosalpha

If sin theta sin(2 alpha+theta)sin(4 alpha+theta),......sin(2(n-1)alpha+theta)=(sin theta)/(2n-1) where 2n alpha=pi then cot(theta)+cot(2 alpha+theta)+cot(4 alpha+theta)+......+cot(2(n-1)alpha+theta))=

Prove that : 2 sin^2 theta + 4 cos (theta + alpha) sin alpha sin theta + cos 2 (alpha + theta) is independent of theta.