I hadn't seen the tutorial, but the presentation had the same angular differences example. I see the point, but don't find it compelling because of the contrived nature of the manual testing. E.g. the "bad" manual example only uses positive numbers, and never bothers to test the obvious edge case:

return abs($a - $b) % 180
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This edge case is either side of the modulo 180, and a quick examination of the code (without even testing) shows that it's impossible to ever have an angular difference of 180 degrees. Even ignoring the code for a moment, the real edge cases that thoughtful manual testing should have checked are the edges of acceptable output -- zero angular difference and 180 degrees of angular difference.

At a certain point in the tutorial, the author refines the problem as so:

If you think about it, our recipe above is actually a specification of a general property that our implementation must hold to: "For all angles a and for all angles diff in the range -180 to 180, we assert that angdiff($a, $a + $diff) must equal abs($diff)."

Testing differences of -180, -1, 0, 1, and 180 is sufficient -- the random testing in between doesn't add additional information. (And this principle extends to the later example of differences greater than 180 or even 360 degrees.) My point is that if you understand the problem space well enough and specify the expectation well enough, ordinary tests are easily sufficient. So you can use Test::LectroTest, or just this:

for ( -180, -1, 0, 1, 180 ) {
    is( angdiff(0, $_), abs $_, "angdiff (0,$_)" );
}
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Let me be fair -- I think Test::LectroTest could be a very useful tool for exploring a poorly understood problem space by generating lots of test cases for examination, but I wouldn't use it as a first-line-of-defense testing tool.