Make sure your calculator is in radian mode.

$−0.76$

$\text{Since }\frac{4\pi}{3} \text{ is related to the }30^\circ-60^\circ-90^\circ\text{ angles, this one}$

$\text{has an exact answer. Locate it on the unit circle.}$

$\text{Notice that it will be a reflection (twice) of sin} \left(\frac{\pi}{3}\right).$

It is in the third quadrant.