`4cos^2xsinx - 2sin^2x = 3sinx`
`=>sinx(4cos^2x - 2sinx -3) = 0`
`=>sinx(4(1-sin^2x) - 2sinx -3) = 0`
`=>sinx(4-4sin^2x - 2sinx -3) = 0`
`=>-sinx(4sin^2x + 2sinx -1) = 0`
`=>-sinx = 0 or 4sin^2x + 2sinx -1 = 0`
`=>sinx = 0 or sinx = (-2+-sqrt(4-4(4)(-1)))/8`
`=>sinx = 0 or sinx = (-1+-sqrt5)/4`
`=>sinx = sin 0^@ or sinx = sin18^@ or sinx = sin (-54^@)`
`=>x = npi or x = npi+(-1)^n(18^@) or x = npi+(-1)^n(-54^@)`
So, these are the three solutions for the given equation.
