All life on Earth is based on one of many two-polymer systems, each made up of a protein and a nucleic acid. In a cell, these polymers are, for the most part, charge-balanced, with the nucleic acid in any pair carrying a negative charge and the protein carrying an equal amount of positive charge. Consider a distribution of eight of these polymers, where the eight proteins sit together near the center of the cell and the nucleic acids are spread out along the circumference of a circle with the radius equal to one-quarter of the cell diameter, centered on the proteins. If seven of the eight nucleic acids are at \(\pi / 4, \pi / 2,3 \pi / 4, \pi, 3 \pi / 2,7 \pi / 4\), and \(2 \pi \mathrm{rad}\), where on the circle must you place the eighth acid to give the system a balanced charge distribution? (Begin by making a sketch.)