Now you compute the true bearing for north/south line.

Did your bearing compute to be North 0 degrees, 03 minutes West? Your theta should have equaled 0 degrees, 03 minutes.

Since two-point control relies primarily on record distances with no correction exerted by points beyond the lost point, it is not truly a proportionate method. But the application of an index correction for average error, as shown, will in many situations give nearly the same results as a true proportion, if a proportion were possible.