Answer
$\theta = 45˚, 135˚,225˚, 315˚$
Work Step by Step
$\tan \theta - \cot \theta = 0$
$\frac{\sin \theta}{\cos \theta} - \frac{\cos \theta}{\sin \theta} = 0$
$\frac{(\sin \theta)^{2}- (\cos \theta)^{2}}{\cos \theta \sin \theta} = 0$
$(\sin \theta)^{2}- (\cos \theta)^{2} = 0$
$-[-(\sin \theta)^{2}+ (\cos \theta)^{2}] = 0$
$-[(\cos \theta)^{2}-(\sin \theta)^{2}] = 0$
$-cos(2\theta) = 0$
$cos(2\theta) = 0$ (Since its $2\theta$, then its for 2 cycles)
$2\theta = 90˚, 270˚, (90˚ + 360˚), (270˚ + 360˚)$
$2\theta = 90˚, 270˚, 450˚, 630˚$
$\theta = \frac{90}{2}˚, \frac{270}{2}˚, \frac{450}{2}˚, \frac{630}{2}˚$
$\theta = 45˚, 135˚,225˚, 315˚$
