What is the general solution for 3sin(θ)=sin(θ)-sqrt(2) ?

The general solution for 3sin(θ)=sin(θ)-sqrt(2) is θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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3sin(θ)=sin(θ)-sqrt(2)

3 sin (θ) = sin (θ) - 2

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Solution steps

3 sin (θ) = sin (θ) - 2

Solve by substitution

sin (θ) = - \frac{2}{2}

sin (θ) = - \frac{2}{2} : θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Combine all the solutions

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

sec^{2} (x) - 2 sec (x) + 1 = 0

cos (θ) = sin (θ - \frac{π}{3})

[sin (x) + \frac{1}{2}]^{2} = \frac{1}{2} sin (x) + \frac{13}{16}

- csc (x) + 2 csc^{3} (x) = 0

sin (θ) = \frac{500}{680}

What is the general solution for 3sin(θ)=sin(θ)-sqrt(2) ?
The general solution for 3sin(θ)=sin(θ)-sqrt(2) is θ=(5pi)/4+2pin,θ=(7pi)/4+2pin