f(x)=[sinxsin(π/3-x)]/[2sin^2 (2π/3) ]
2sin^2 (2π/3)=3/2
sinxsin(π/3-x)=4分之根号3*sin2x-（1-cos2x）/4=1/2*sin（2x+π/6）-1/4
f(x)=[1/2*sin（2x+π/6）-1/4]/(3/2)=1/3*sin（2x+π/6）-1/6
g（x)=6mf(x)+1=6m*[1/3*sin（2x+π/6）-1/6]+1=2m*sin（2x+π/6）-m+1
x∈(0,π/3) 2x+π/6∈(π/6,5π/6)
sin（2x+π/6)∈(1/2,1]
g（x)=2m*sin（2x+π/6）-m+1∈(1,m+1]
函数g（x）的值域为（1,5/4]
m+1=5/4,m=1/4