Does anybody have a reference answering the following (at least for me surprisingly non trivial) question?

Given an $n \times n$ integer grid, what is the minimum angle between any two distinct lines, each going through some grid point $p$ and at least one other grid point?

I asked this a few years back on [MSE][1] and am still interested in a pointer / reference to a proof.


  [1]: http://math.stackexchange.com/questions/111727/smallest-angle-among-two-lines-in-n-times-n-grid