sin^2α+cos^2(π/6+α)+1/2sin^2(α+π/6)
=1/2(1-cos2α)+1/2[1+cos(π/3+2α)]+[1-cos(π/3+2α)]
=-1/2cos2α-1/2cos(π/3+2α)+2
=-1/2cos2α--1/4cos2α+√3/4sin2α+2
=√3/4sin2α-3/4cos2α+2
=√3/2(1/2sin2α-√3/2cos2α)+2
=√3/2sin(2α-π/3)+2