Answer
-2
Work Step by Step
$\frac{2\pi}{3}$ radians= $\frac{2\times180}{3}^{\circ}=120^{\circ}$
$120^{\circ}$ is in the second quadrant and secant function is negative in the second quadrant.
As $\theta$ is in quadrant II, the reference angle is
$\theta'=180^{\circ}-\theta=180^{\circ}-120^{\circ}=60^{\circ}$
$\sec\frac{2\pi}{3}=\sec120^{\circ}=-\sec60^{\circ}$
$=-\frac{1}{\cos 60^{\circ}}=-\frac{1}{\frac{1}{2}}=-2$
