Prove that: `cos^2A+cos^2(A+(2pi)/3)+cos^2(A-(2pi)/3)=3/2`

Explanation

Here we use `cos^(2)A -sin^(2)B= cos(A+B)cos(A-B)`
LHS`=cosp^(2)theta +cos^(2)((2pi)/(3)-theta)+1-sin^(2)((2pi)/3+theta)+1`
Use `cos^(2)A-sin^(2)B=cos(A+B)cos(A-B)`
`=(cos^(2)theta+cos(4pi)/(3) cos 2theta+1)`
`cos^(2)theta+cos(pi+pi/3) cos2theta+1`
`cos^(2)theta-1/2 cos2theta+1`
`cos^(2)theta-1/2(2cos^(2)theta-1)+1`
`=1/2+1=3/2`