What is the general solution for cot^2(θ)=cot(θ),0<= θ<= 2pi ?

The general solution for cot^2(θ)=cot(θ),0<= θ<= 2pi is θ= pi/4 ,θ=(5pi)/4 ,θ= pi/2 ,θ=(3pi)/2

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cot^2(θ)=cot(θ),0<= θ<= 2pi

cot^{2} (θ) = cot (θ), 0 \leq θ \leq 2 π

θ = \frac{π}{4}, θ = \frac{5 π}{4}, θ = \frac{π}{2}, θ = \frac{3 π}{2}

Solution steps

cot^{2} (θ) = cot (θ), 0 \leq θ \leq 2 π

Solve by substitution

cot (θ) = 1, cot (θ) = 0

cot (θ) = 1, 0 \leq θ \leq 2 π : θ = \frac{π}{4}, θ = \frac{5 π}{4}

cot (θ) = 0, 0 \leq θ \leq 2 π : θ = \frac{π}{2}, θ = \frac{3 π}{2}

Combine all the solutions

θ = \frac{π}{4}, θ = \frac{5 π}{4}, θ = \frac{π}{2}, θ = \frac{3 π}{2}

cos (x) = \frac{9}{19}

cos (α) = \frac{5}{3}

2 - 3 sin (x) - cos (2 x) = 0

cos (2 θ) = \frac{1}{4}

sec (θ) = \frac{25}{7}

What is the general solution for cot^2(θ)=cot(θ),0<= θ<= 2pi ?
The general solution for cot^2(θ)=cot(θ),0<= θ<= 2pi is θ= pi/4 ,θ=(5pi)/4 ,θ= pi/2 ,θ=(3pi)/2