`(sin 3x + cos 3x)^2 + sqrt{3}cos 6x = 2`
`<=> sin^2 3x + cos^2 3x + 2sin 3x.cos 3x + sqrt{3}cos 6x = 2`
`<=> 1 + 2sin 3x.cos 3x + sqrt{3}cos 6x = 2`
`<=> sin 6x + sqrt{3}cos 6x = 1`
`<=> 2.sin (6x + π/3) = 1`
`<=> sin (6x + π/3) = sin (π/6)`
`<=>` \(\left[ \begin{array}{l}6x + \dfrac{π}{3} = \dfrac{π}{6} + k2π\\6x + \dfrac{π}{3} = \dfrac{5π}{6} + k2π\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = -\dfrac{π}{36} + k\dfrac{π}{3}\\x = \dfrac{π}{2} + k\dfrac{π}{3}\end{array} \right.\) `(k ∈ ZZ)`
