The third and fourth terms of a geometric progression are \(\frac { 1 } { 3 }\) and \(\frac { 2 } { 9 }\) respectively. Find the sum to infinity of the progression.
A circle is divided into 5 sectors in such a way that the angles of the sectors are in arithmetic progression. Given that the angle of the largest sector is 4 times the angle of the smallest sector, find the angle of the largest sector.