Can't edit the above post, but when trying to write this up more carefully I realized it's not correct: (1) For one thing, the difference in epsilon is very sm

Can't edit the above post, but when trying to write this up more carefully I realized it's not correct: (1) For one thing, the difference in epsilon is very small: the ratio (1 + ε√3)/(1 - ε√3) is 1+2√3ε+O(ε²), that is, we're comparing something like 4ε+4√3ε² versus 4ε-4√3ε², which is probably too small to matter. (2) The argument looks like it applies to all angles, but in fact experimentation shows the same phenomenon does not appear, and finally, (3) Here are the next two terms after: (211,14), (94,191): 60.000000269 (253,140), (1,55): 59.999999869 (265,71), (41,153: 60.000000035 where we see that one term is less than 60 degrees.