关于x的方程sinx-根号3cosx=4m-6/4-m有解,求m的取值范围

sinx-根号3cosx=4m-6/4-m
2sin(x-π/3)=(4m-6)/(4-m)
-2≤(4m-6)/(4-m)≤2
(4m-6)/(4-m)≥-2
(4m-6+8-2m)(m-4)≤0
(2m+2)(m-4)≤0
-1≤m<4
(4m-6)/(4-m)≤2
(4m-6-8+2m)(m-4)≥0
(6m-14)(m-4)≥0
m≤7/3 或 m>4
取交集得-1≤m≤7/3