## Precalculus (6th Edition)

$-\displaystyle \frac{\sqrt{6}}{6}$
Letting $A=2x,$ we express $x=\displaystyle \frac{A}{2},\quad \displaystyle \sin x=\sin\frac{A}{2}$ $( \sin x$ is negative, as $x$ terminates in Q.III.) Half-Angle identity: $\displaystyle \sin\frac{A}{2}=-\sqrt{\frac{1-\cos A}{2}}=-\sqrt{\frac{1-(\frac{2}{3})}{2}}$ $=-\displaystyle \sqrt{\frac{3-2}{6}}=-\frac{1}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}}$ $=-\displaystyle \frac{\sqrt{6}}{6}$