f'(x)=[2cosx＋1]/[(2＋cosx)²].在[2kπ－2π/3,2kπ＋2π/3]上递增,在[2kπ＋2π/3,2kπ＋4π/3]上递减.设g(x)=f(x)－(1/3)x,则g'(x)=f'(x)－1/3.由f(x)的单调,确定g(x)的最小值大于0即可.