Presumably you've got to the equation sin2θ = -1 (based on the fact that you've got the solution 3π/4, correct me if I'm wrong).
Now 0<θ<2π => 0<2θ<4π. sin2θ would then have two values equal to -1.
From here, you should work out the other answer.
TL:DR, In this case, you want to check beyond the 0 to 2π range, depending on what's inside the trig. function.
