First, let's note that the issue here really has nothing to do with whether nature is unique. If "nature" in the sense used here was not unique, one might still expect to use "a". The question is not why we use "a" instead of "the", but why we use no article at all.
The reason is because we are not speaking of "nature" as an entity but rather as a general idea. When we use words speaking of an idea, we don't use articles.
Consider the very similar sentence, "The laws of a nation are approximate." (I don't know what that would mean but that's not the point here.) We are speaking of a nation as an entity, a thing, so we must use an article. (Or certain alternative words, like a possessive pronoun, e.g. "my nation".)
But when you speak of a general idea, a concept, you don't use an article. For example, I might say, "Art uplifts people." I don't say "An art uplifts people", because I am not talking about individual works of art, but about the general idea. (Maybe this is a bad example because I could say, "The art uplifts people". But then I'm referring to a specific set of works of art. Hopefully identified by the context. Like, "There are many great works of art in the Louvre. The art uplifts people.")
So we don't say, "The nature is beautiful", but "Nature is beautiful."
I guess like "the art", you could say "the nature" if you were using the word "nature" in a different sense. Like, "The nature of dogs is to be loyal." Here we're not talking about nature as a general concept, the universe as it exists or would exist if untouched by humans, but rather we're using "nature" to mean "characteristic state or behavior". Really an entirely different definition.