#### Answer

$\{135^{o}, \ \ 225^{o}\}$

#### Work Step by Step

For a point on the unit circle, the coordinates are
($\cos\theta,\sin\theta),\ \quad \theta\in[0^{o},360^{o})$
To solve the problem, find the points for which
the $x$-coordinate is $-\displaystyle \frac{\sqrt{2}}{2},\ \quad$($\displaystyle \cos\theta=-\frac{\sqrt{2}}{2}$).
Using the given unit circle, we find two such points,
in quadrant II, for $\theta=135^{o}$
in quadrant III, for $\theta=225^{o}$
Solution set: $\{135^{o}, \ \ 225^{o}\}$