I'm working through the section in baby Hartshorne on Archimedian Neutral Geometry, and I've been stuck for a couple of days trying to (synthetically) prove the following: In a Hilbert plane satisfying Archimedes' axiom where the parallel postulate is false, given an angle $\epsilon \gt 0$, show that there exists a triangle with angles $\alpha, \beta, \gamma$, all three smaller than $\epsilon$.
There was even a hint to use an earlier exercise (which I have already proved), namely: For any angle $\alpha$, however small, there exists a line $l$ entirely contained in the inside of the angle. Also, we have already proved Saccheri-Legendre. I remain stuck. Any assistance would be welcome. Thanks.