I have a ± in that last step, and it will be + in some quadrants
and negative in others. So we must decide which it is for θ in
quadrant 3.

The tangent is positive in quadrant 3, so we must make sure
to choose the sign of the last expression so that it is
positive in quadrant 3.  

The square root is positive, but the cosine is negative in
quadrant 3, so we must choose the sign as negative to make
the expression on the right come out positive for θ in 
quadrant 3.



Edwin