Solution: The equation $ \sin(2\theta) = \frac\sqrt32 $ implies $ 2\theta = 60^\circ + 360^\circ k $ or $ 2\theta = 120^\circ + 360^\circ k $ for integer $ k $. Solving for $ \theta $, we get $ \theta = 30^\circ + 180^\circ k $ or $ \theta = 60^\circ + 180^\circ k $. Within $ [0^\circ, 360^\circ] $, the solutions are $ 30^\circ, 60^\circ, 210^\circ, 240^\circ $. Thus, the answer is $ \boxed30^\circ, \boxed60^\circ, \boxed210^\circ, \boxed240^\circ $. - Abu Waleed Tea