\(\dfrac{{\sqrt 3 }}{2}\)

\begin{aligned}
\sin \left(-300^{\circ}\right) &=-\sin \left(300^{\circ}\right) \\
&=-\sin \left(360^{\circ}-60^{\circ}\right) \\
&=+\sin 60^{\circ}\\
&=\frac{\sqrt{3}}{2}
\end{aligned}