What is the general solution for sin^2(θ)-sin(θ)-2=0 ?

The general solution for sin^2(θ)-sin(θ)-2=0 is θ=(3pi)/2+2pin

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sin^2(θ)-sin(θ)-2=0

sin^{2} (θ) - sin (θ) - 2 = 0

θ = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (θ) - sin (θ) - 2 = 0

Solve by substitution

sin (θ) = 2, sin (θ) = - 1

sin (θ) = 2 :

No Solution

sin (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn

tan (2 θ) = 3

sin^{2} (x) - 6 cos (x) - 6 = 0

(3 tan^{2} (x) - 1) = 0

8 sin (\frac{x}{2}) - 8 = 0

cos (2 x) + 2 = 3 cos (x)

What is the general solution for sin^2(θ)-sin(θ)-2=0 ?
The general solution for sin^2(θ)-sin(θ)-2=0 is θ=(3pi)/2+2pin