Evaluate the infinite sum: ∑n=1∞arctan(12n2)\sum_{n=1}^{\infty} \arctan\left(\frac{1}{2n^2}\right)∑n=1∞arctan(2n21).
π4\frac{\pi}{4}4π
π2\frac{\pi}{2}2π
π\piπ
arctan(1)\arctan(1)arctan(1)