The condition that dependent variables must be "continuous and unbounded" is unusual: there is no mathematical or statistical requirement for either.
In most regression models we posit that the dependent variable be a linear combination of the independent variables plus an independent random error term of zero mean, approximately and within the ranges attained by, or potentially attained by, the independent variables. For instance, it would be fine to regress the length of the Mississippi River on time for the period 1700 - 1850 but not to project the regression back, say, a million years or forward 700 years:
In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.
(Mark Twain, Life on the Mississippi.)
In the present case it sounds like the angle is an independent variable, not the dependent one, so this question does not even arise. The problem that arises is that the angle seems to be defined only modulo 360 degrees (actually mod 180). Actually, the angle is really a latitude and varies from 0 to 180 (or -90 to 90) without "wrapping around" at all. Really, then, all that matters is how best to express this angle: does the reaction rate vary linearly with the angle or does it vary perhaps with its sine or cosine? Or maybe its tangent, which is unbounded? But that matter is addressed with appropriate exploratory analysis, perhaps by some stereochemical considerations, and standard procedures to fit and check models. Therefore this angular variable neither enjoys nor suffers from any special quality that would distinguish it from other independent variables.