Answer
$\{0^{o},180^{o}\}$
Work Step by Step
$\cos^{2}\theta-\sin^{2}\theta =1$
... recognize a double angle (cosine) identity
$\cos 2\theta=1$
If $0 \leq \theta < 360^{o}\quad/\times 2$
$0 \leq 2\theta < 720^{o}$
$ 2\theta=0^{o}\quad$ or $\quad 2\theta=360^{o}$
$\theta=0^{o}\quad$ or $\quad \theta=180^{o}$
Solution set= $\{0^{o},180^{o}\}$
