The author has always been fascinated by the title identity. It's charming and simple, as well as easy to believe after pressing a few calculator keys. Several fine proofs have appeared in the literature, including several proofs without words. His own earlier proof is trigonometric, and he has often been dissatisfied with not being able to produce his own simple, direct, purely geometric proof. In this paper, the author offers both trigonometric and geometric proofs of Arctan1 + Arctan2 + Arctan3 = [pi], as well as a unifying puzzle.