Question

Find the solutions of the equation that are in the interval [0, 2π). (enter your answers as a comma-separated list. if there is no solution, enter no solution.) cot2 θ + cot θ = 0

Answer 1

Hello : 
cot (2 θ) + cot ( θ) = 0
cot (2 θ) = -  cot ( θ) 
cot (2 θ) = cot ( - θ)
2 θ = - θ +2k π    k   in : Z
θ = 2k π /3
in : [0, 2π)
k=0 : θ = 0
 k=1 : θ = 2π /3
k=2 : θ = 4π /3