`sin x + \sqrt{3} cos x = \sqrt{2}`
`⇔ sin x = \sqrt{2} - \sqrt{3} cos x`
`⇔ sin^2 x = (\sqrt{2} - \sqrt{3} cos x)^2`
`⇔ sin^2 x - 2 + 2\sqrt{6} cos x - 3cos^2 x = 0`
`⇔ -1-4 cos^2 x + 2cos x\sqrt{6} = 0`
`⇔ cos x = (\sqrt{6}\pm\sqrt{2})/4`
`⇔ x= arccos((\sqrt{6}-\sqrt{2})/4) + 2πn , x= 2π - arccos((\sqrt{6}+\sqrt{2})/4) + 2πn`