Answer
$\frac{4\pi}{3},\frac{5\pi}{3}$
Work Step by Step
Using trigonometric identities, we have
$4sin\theta+3\sqrt 3=\sqrt 3 \longrightarrow sin\theta=-\frac{\sqrt 3}{2} \longrightarrow \theta=\pi+\frac{\pi}{3},2\pi-\frac{\pi}{3} \longrightarrow \theta=\frac{4\pi}{3},\frac{5\pi}{3}$