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Take the inverse sin of both sides and then solve for θ.

do you know how to solve sin(x)=-1 on 0 <=x<6pi?

if not do you know how to solve sin(x)=-1 on 0<=x<2pi?

at 3pi/2

yes

and what we actually want to solve for is theta not x

so replace x with 3 theta

and solve the linear equations

did you have any questions ?

sin* not sign

well you will have 3 solutions not just one

Ah yes, but that can be done by cumulatively adding 2pi before dividing by 3. One extra step.