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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.