Answer
$-\dfrac{2\sqrt3}{3}$
Work Step by Step
We know that $\sin$, $\csc$, $\tan$ are odd functions, which means $f(-\theta)=-f(\theta).$
We also know that $\cos$, $\sec$, are even functions, which means $f(-\theta)=f(\theta).$
Therefore,
$\csc{\left(-\frac{\pi}{3}\right)}\\
=-\csc{\left(\frac{\pi}{3}\right)}\\
=-\dfrac{1}{\sin(\frac{\pi}{3})}\\
=-\dfrac{1}{\frac{\sqrt3}{2}}\\
=-\frac{2}{\sqrt3}\\
=-\frac{2}{\sqrt3} \cdot \frac{\sqrt3}{\sqrt3}\\
=-\frac{2\sqrt3}{3}$
