Let $v$ and $w$ be distinct, randomly chosen roots of the equation $z^{1997}-1=0.$  Find the probability that
\[\sqrt{2+\sqrt{3}}\le\left|v+w\right|.\]
Question:
Let $v$ and $w$ be distinct, randomly chosen roots of the equation $z^{1997}-1=0.$  Find the probability that
\[\sqrt{2+\sqrt{3}}\le\left|v+w\right|.\]
Answer:
Let's think step by step.

user
\frac{83}{499}
Let $v$ and $w$ be distinct, randomly chosen roots of the equation $z^{1997}-1=0.$  Find the probability that
\[\sqrt{2+\sqrt{3}}\le\left|v+w\right|.\]
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