Question

how would you solve 3sin0=sin0-1

Answer 1

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.

Answer 2

           3sinΘ = sinΘ - 1
3sinΘ - sinΘ = sinΘ - sinΘ - 1
           2sinΘ = -1
            2sin     2sin
               Θ = -2.864934497