(cosx)^6-(sinx)^6
=[(cosx)^3+(sinx)^3][(cosx)^3-(sinx)^3]
=(cosx+sinx)*(cos^2x-sinxcosx+sin^2x)(cosx-sinx)(cos^2x+sinxcosx+sin^2x)
=(cosx+sinx)(cosx-sinx)(1-1/2sin2x)(1+1/2sin2x)
=(cos^2x-sin^2x)(1-1/2sin2x)(1+1/2sin2x)
=cos2x*[1-1/4sin^2(2x)]
=cosπ/6*(1-1/4sin²π/6)
=√3/2×(1-1/4×1/4)
=√3/2×15/16
=15√3/32