Minimum difference of angles between points on square lattice I have integer grid of size $N \times N$.

If I calculate angles between all point triples - is it possible analytically find minimal non-zero difference between those angles?
By brute force, for $N = 4, 5, 6$ the smallest non-zero angle is formed between the segments from $(N-1,N-2)$ to $(0,0)$ and from $(N-1,N-2)$ to $(1,1)$, if the coordinates have range $0$ to $N - 1$ inclusive.

The first segment makes an angle
$\theta_1 = \tan^{-1}\left(\frac{N-2}{N-1}\right)$
with the edge of the lattice, and the second segment makes an angle
$\theta_2 = \tan^{-1}\left(\frac{N-3}{N-2}\right)$
with that edge.
The magnitude of the resulting angle between these segments is 
$$| \,\theta_1 - \theta_2| = 
 \tan^{-1}\left(\frac{N-2}{N-1}\right) - \tan^{-1}\left(\frac{N-3}{N-2}\right).
$$
(Since $0 &lt; \theta_2 &lt; \theta_1 &lt; \frac{\pi}{4}$, the right-hand side of this equation is positive.)

While this exercise suggests that this might be the formula for larger $N$ as well, it is hardly a proof. I too am curious about the general result now.
Isn't the minimum angle just the one who's arms are along the diagonal (1,1) to (N,N) the back down to (1,2)? This gives the minimum angle as pi/4 - arctan((N-1)/N).