Prove that: `4\ costhetacos\ (pi/3+theta)cos(pi/3-theta)=cos3theta`

Prove that: 2cos theta cos((pi)/(3)+theta)cos((pi)/(3)-theta)=cos3 theta

The sum of all the solution of the equation costhetacos(pi/3+theta)cos(pi/3-theta)=1/4theta in [0,6pi]

Prove that cos theta +cos ((2pi)/(3)-theta)+cos ((2pi)/(3)+theta)=0

Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=0

The sum of all the solution is of the equation cos theta cos ((pi)/3+theta)cos ((pi)/3-theta)=1/4, theta in [0,6pi ]

Prove that (cos(pi +theta)cos (-theta))/(cos(pi-theta) cos (pi/2+theta))=-cot theta

Prove that (cos(pi+theta)cos(-theta))/(cos(pi-theta)cos((pi)/(2)+theta))=-cot theta

Prove that cos theta + cos[(2pi)/3 + theta] + cos [(4pi)/(3) + theta] = 0 .