已知sin(a+π/3)+sina=-4√3/5,-π/2

sinacosπ/3+cosasinπ/3+sina=-4√3/5
sina*3/2+cosa*√3/2=-4√3/5
√3(sina*√3/2+cpsa*1/2)=-4√3/5
sinasinπ/3+cpsacosπ/3=-4/5
cos(π/3-a)=-4/5
则cos(a+2π/3)
=-cos[π-(a+2π/3)]
=-cos(π/3-a)
=4/5