Let $$v$$ and $$w$$ be distinct, randomly chosen roots of the equation $$z^{1997}-1=0$$. Let $$m/n$$ be the probability that $$\sqrt{2+\sqrt{3}}\le |v+w|$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

(第十五届AIME1997 第14题)