In a circle with radius 1 a regular n-gon $A_1 A_2...A_n$ is inscribed. Calculate the product: $A_1 A_2.A_1 A_3 \dots A_1 A_{n-1} .A_1 A_n$.
Problem
Source: III International Festival of Young Mathematicians Sozopol 2012, Theme for 10-12 grade
Tags: geometry, regular polygon