#### Answer

$\{45^{o},135^{o},225^{o},315^{o}\}$

#### Work Step by Step

Substituting t$=\tan\theta$ ,the equation becomes
$t-\displaystyle \frac{1}{t}=0,\qquad t\neq 0$
$t-\displaystyle \frac{1}{t}=0\quad/\times t$
$t^{2}-1=0$
... difference of squares ...
$(t+1)(t-1)=0$
... apply the zero factor principle...
$ t=1\quad$or$ \quad t=-1$
$\tan\theta=1\quad$or$ \quad\tan\theta=-1$
$\theta=45^{o},225^{o}\quad$or$ \quad \theta=135^{o},315^{o}$
Solution set= $\{45^{o},135^{o},225^{o},315^{o}\}$