答案：cosx=-1 或 cosx=1/4
根据和差化积公式,
[sin(x+120°)-sin(x-120°)]/sin(x+120°)*sin(x-120°)=4根号3/3,
(2cosxsin120°)/[(cos240°-cos2x)/2]=4根号3/3,
化简：2cos2x+3cosx+1=0
2(2cos²x-1)+3cosx+1=0
所以,4cos²x+3cosx-1=0
(cosx+1)(4cosx-1)=0
所以,cosx=-1 或 cosx=1/4