If you draw a unit-radius circle, then in that 3rd quadrant, pick a point on the circumference.
draw a right-angled triangle by drawing lines from the point directly up to the x-axis
and directly from the point to the circle centre.
For this triangle, angle at the centre inside the triangle.
Draw a second right-angled triangle, whose base is and whose opposite is in that same 3rd quadrant
which is the angle after one revolution in the 3rd quadrant.
There is another angle in the 2nd quadrant, as cosine is negative there also.
From there, the range of angles can be deduced from