2014 AIME II Problem 10

Let z be a complex number with |z|=2014. Let P be the polygon in the complex plane whose vertices are z and every w such that \frac{1}{z+w}=\frac{1}{z}+\frac{1}{w}. Then the area enclosed by P can be written in the form n \sqrt{3}, where n is an integer. Find the remainder when n is divided by 1000 .