Degrees or Rads? No difference!

That was fun; I hadn't come across that angle before. I got this on my third attempt, but one of my attempts was $0$ , so you may want specify "the smallest positive angle" to avoid any potential ambiguity. I suppose the technical issue with $0$ as a potential answer would be what happens with the cosecant and cotangent function as the angle(s) approach $0$ . The results do in fact match in both cases, but this would involve a proof involving limits, which I don't think is what you had in mind, so it's probably easiest if you just specify the angle as being positive. :)

@Guiseppi Butel I've just tried your Problem #2, and I have a couple of questions. Technically there can be no "smallest negative angle"; I think that you might mean "the largest negative angle", or similarly "the negative angle with the least magnitude". For example, the largest negative integer is $-1$ , since it is greater than all other negative integers, but it is also has the smallest magnitude, (i.e., absolute value), among negative integers.

My second question is: are you certain the answer to Problem #2 isn't - $6.395$ ? The solution set I find is all $x$ such that

$x = \dfrac{360*n*\pi}{180 - \pi}$ for any integer $n$ .

This would mean the the magnitude of the answers to the two problems would be the same. Am I missing something?