Evaluate the infinite sum S=∑n=1∞arctan(2n2)S = \sum_{n=1}^{\infty} \arctan\left(\frac{2}{n^2}\right)S=∑n=1∞arctan(n22).
3π4\frac{3\pi}{4}43π
π\piπ
5π4\frac{5\pi}{4}45π
3π2\frac{3\pi}{2}23π