cot (x) - cot^2 (x) = 0 x E [0,2pi]

cot (x) = cot^2(x)

cot (x) = 1

tan (x) = 1

x = tan-1(1)

x = pi/4 + pi*n

I get {pi/4, 5pi/4} but the answer is {pi/2, 3pi/2, pi/4, 5pi/4}

In a lot of these types of questions, I keep getting half the solutions, is there a universal method that would allow me to always find all the possible values no matter the identity?

(I don't know if "identity" is the right word for this since x can't be any value but I don't know what else to call it)

Thanks in advance!