解cosa^2+cos（α+2π/3）^2+cos（α-2π/3)^2
=(1+cos2a)/2+[cos(2a+4π/3)+1]/2+[cos(2a-4π/3)+1]/2
=(1+cos2a)/2+[1-cos(2a+π/3)]/2+[1-cos(2a-π/3)]/2
=(1+cos2a)/2+1-cos2a/2
=3/2