Here. For the last part, we have to include one cycle before 0 to 2 pi (i.e. -2 pi to 0), since solving for cos (theta - something) means that theta - something can go below 0 radians, keeping in mind that a positive output value of cos means that theta - something lies in the first or the fourth quadrant.

As it turns out, this is necessary as the value of theta - something in the first quadrant leads to theta being more than pi/2 (90 degrees), which has to be rejected, leaving us with the other value of theta - something coming from the fourth quadrant.