[tex]2sin(\theta )+\sqrt{3}=0\implies 2sin(\theta )=-\sqrt{3}\implies sin(\theta )=-\cfrac{\sqrt{3}}{2} \\\\\\ sin^{-1}\left[ sin(\theta ) \right]=sin^{-1}\left( -\cfrac{\sqrt{3}}{2} \right) \implies \theta =sin^{-1}\left( -\cfrac{\sqrt{3}}{2} \right)\implies \theta \begin{cases} \stackrel{III~Quadrant}{\frac{4\pi }{3}}\\\\ \stackrel{IV~Quadrant}{\frac{5\pi }{3}} \end{cases}[/tex]
check your Unit Circle.
