Puzzle of the Week #149 - Nazca Polygon

There is a regular 2018-sided polygon engraved in the Nazca Desert in Peru. The corners are alternately coloured red and green. Any pair of opposite corners are exactly 2 miles apart.

You stand on one of the green corners, and measure your straight-line distance to each of the 1009 red corners (in miles). You multiply together all of these distances.

What do you get?


(Maths hint: try smaller numbers of sides first to see if you can detect any pattern.)