Find the area of a triangle with angles $\frac{1}{7} \pi$, $\frac{2}{7} \pi$, and $\frac{4}{7} \pi $, and radius of its circumscribed circle $R=1$.
Problem
Source: III International Festival of Young Mathematicians Sozopol 2012, Theme for 10-12 grade
Tags: area of a triangle, geometry