And to make it even faster

I knew it's wrong because I had made the same mistake in my previous research.

It's bigger, simply because it uses some smaller distance to calculate the radians.

The correct one is:

<math>\theta = \int_0^{t_1} \frac{v_{lateral}}{d_{initial} + v_{retreat} t}dt</math>

where <math>t_1</math> is the total time (from bullet fired, to bullet hit).

Note that <math>d_{initial} + v_{retreat} t</math> is bigger than (his) <math>(v_{bullet} - \overline{v_{retreat}})t_1</math> almost all of the time,

as <math>d_{initial} =

(v_{bullet} - \overline{v_{retreat}})t_1</math>. 

Therefore his integral (<math>\theta = \int_0^{t_1} \frac{\overline{v_{lateral}}}{(v_{bullet} - \overline{v_{retreat}})t_1}dt = \frac{\overline{v_{lateral}}}{v_{bullet} - \overline{v_{retreat}}}</math>) is bigger.