if you write your own sentence, and finish with quote of an entire sentence, why isn't there a period for both sentences? Brian said, "let's go.". I actually d

if you write your own sentence, and finish with quote of an entire sentence, why isn't there a period for both sentences? Brian said, "let's go.". I actually do this sometimes. But I'm not consistent with it. I think it's also correct to say <<Brian said, "let's go".>> [1]. It's correct because we are allowed to quote just a portion of the sentence, which in this case happens to be every word of it. [1] angle quotes just for the clarity that another level of normal quotes would destroy.