What is the general solution for sin^2(θ)=sin(θ)+1-sin^2(θ) ?

The general solution for sin^2(θ)=sin(θ)+1-sin^2(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ= pi/2+2pin

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sin^2(θ)=sin(θ)+1-sin^2(θ)

sin^{2} (θ) = sin (θ) + 1 - sin^{2} (θ)

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{π}{2} + 2 πn

Solution steps

sin^{2} (θ) = sin (θ) + 1 - sin^{2} (θ)

Solve by substitution

sin (θ) = - \frac{1}{2}, sin (θ) = 1

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{π}{2} + 2 πn

sin (x) = 0.75

(cot (θ) - 1) (csc (θ) + 1) = 0

tan (θ) = - \frac{2}{3}

cot^{2} (x) = csc (x) - 1

sin (θ) = - \frac{2}{3}

What is the general solution for sin^2(θ)=sin(θ)+1-sin^2(θ) ?
The general solution for sin^2(θ)=sin(θ)+1-sin^2(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ= pi/2+2pin