Answer
$\color{blue}{s=\dfrac{2\pi}{3}}$
Work Step by Step
RECALL:
(1) $\frac{\pi}{3}$ is a special angle and $\tan{(\frac{\pi}{3})}=\sqrt3$
(2) An angle and its reference angle either have the same trigonometric function values or they differ only in sign.
The required value of $s$ is in the interval $\left[\dfrac{\pi}{2}, \pi\right]$, which is in Quadrant II.
Note that the reference angle of $\dfrac{2\pi}{3}$ is $\dfrac{\pi}{3}$, and that since $\dfrac{2\pi}{3}$ is in Quadrant II, its tangent value is negative,
Thus, if $\tan{s} = -\sqrt{3}$ and $s$ must be in $\left[\dfrac{\pi}{2}, \pi\right]$, then $\color{blue}{s=\dfrac{2\pi}{3}}$.
