已知：√3sinα+cosα=2√3/3,则：√3/2*sinα+1/2*cosα=√3/3＝cos(π/6)*sinα+sin(π/6)*cosα＝sin(α+π/6)=√3/3；则：[sin(α+π/6)]^2=1/3因为：cos(2α+π/3)=cos2(α+π/6)＝1-2[(sin(α+π/6)]^2=1-2*1/...