Number of integral value(s) of `m` for which the equation `sinx-sqrt(3)cosx=(4m-6)/(4-m)` has solutions, `x in [0,2pi]` , is ________

Explanation

`asinx+bcosx`

`sinx-sqrt3cosx=(4m-6)/(4-m)`

`2(1/2sinx-sqrt3/2cosx)=(4m-6)/(4-m)`

`2(cospi/3*sinx-sinpi/3*cosx)=(4m-6)/(4-m)`

`2(sin(x-pi/3))=(4m-6)/(4-m)`

`sin(x-pi/3)=(2m-3)/(4-m)`

`-1<=sin(x-pi/3)<=1`

`-1<=(2m-3)/(4-m)<=1`

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