`2sin^2x + \sqrt{3}.sin2x = 3 `
`-> 2sin^2x - 1 + sqrt{3}sin2x = 2 `
`-> -(1 - 2sin^2x) + \sqrt{3}.sin2x = 2 `
`-> -cos2x + sqrt{3}.sin2x = 2`
`->sqrt{3}.sin2x - cos2x = 2 `
`->\sqrt{3}/2.sin2x - 1/2.cos2x = 1 `
`-> cos\pi/6.sin2x - sin\pi/6.cos2x = 1 `
`-> sin( 2x - \pi/6 ) = 1 `
`-> 2x - \pi/6 = \pi/2 + k2\pi (k∈Z)`
`-> ``2x` `=` `2\pi/3` `+` `k2\pi`
`-> x = \pi/3 + k\pi`
`->``D.` `x=` `\pi/3` `+` `k\pi` `,` `k∈Z`