Answer
$\theta=135^{\circ}$ or $225^{\circ}$
Work Step by Step
1. Since $sec\theta$ is negative, $\theta$ must be in quadrant II or III.
2. The absolute value of $sec\theta$ is $\sqrt 2$, therefore the reference angles is $45^{\circ}$.
The actual angles in II and III quadrants are following:
$180^{\circ}-45^{\circ}=135^{\circ}$
$180^{\circ}+45^{\circ}=225^{\circ}$
