How would you solve 3sin0=sin0-1

3sinΘ = sinΘ - 1

3sinΘ - sinΘ = sinΘ - sinΘ - 1

2sinΘ = - 1

2sin 2sin

Θ = - 2.864934497

I would subtract 1sin (Θ) from each side of the equation.

The equation would then say that 2sin (Θ) = - 1.

I would only have to find angles whose sin is - 1/2,

and those would be my solutions.