化简cosθ+cos(θ+2π/3）+cos(θ+4π/3）急！！在线等！！！！

cosθ+cos(θ+2π/3）+cos(θ+4π/3）
=cosθ+cosθcos2π/3-sinθsin2π/3+cosθcos4π/3-sinθsin4π/3
=cosθ-1/2*cosθ-√3/2*sinθ-1/2*cosθ+√3/2*sinθ
=0

cosθ+cos(θ+2π/3）+cos(θ+4π/3）
=cosθ+cosθcos2π/3-sin2π/3-cos(θ+π/3）
=cosθ-1/2cosθ+√3/2sinθ-cosθcosπ/3+sinθsinπ/3
=cosθ-1/2cosθ+√3/2sinθ-1/2cosθ+√3/2sinθ
=√3sinθ

cosθ+cos(θ+2π/3）+cos(θ+4π/3）
= cosθ+cosθ·（-1/2） - 根3cosθ/2 - cos（θ+π/3）
=cosθ+cosθ·（1-/2）-根3cosθ/2 - cosθ/2 +根3cosθ/2
=0

解：原式=cosα+cos[π-(π/3-α)]+cos[π+(π/3+α)]
=cosα-[cos(π/3-α)+cos(π/3+α)]
=cosα-(cosπ/3cosα+sinπ/3sinα+cosπ/3cosα-sinπ/3sinα)
=cosα-2cosαcosπ/3
=0

答案是0