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Solving Equations of the Binomial Form (Cotangent)

TRIG-XYVXNU

Solve the following equation on the interval $[0, 2\pi)$:

$$\cot^2{\theta}+\cot{\theta}=0$$

A

$0, \pi, \cfrac{\pi}{2}, \cfrac{3\pi}{2}$

B

$\cfrac{\pi}{2}, \cfrac{3\pi}{2}, \cfrac{\pi}{6}, \cfrac{5\pi}{6}$

C

$0, \pi, \cfrac{3\pi}{4}, \cfrac{7\pi}{4}$

D

$\cfrac{\pi}{2}, \cfrac{3\pi}{2}, \cfrac{\pi}{4}, \cfrac{5\pi}{4}$

E

$\cfrac{\pi}{2}, \cfrac{3\pi}{2}, \cfrac{3\pi}{4}, \cfrac{7\pi}{4}$