2009 AIME II Problem 13

Let A and B be the endpoints of a semicircular arc of radius 2. The arc is divided into seven congruent arcs by six equally spaced points C_1,C_2,\ldots ,C_6. All chords of the form \overline{AC_i} or \overline{BC_i} are drawn. Let n be the product of the lengths of these twelve chords. 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.