MIT AI Memo 239, Feb. 29, 1972. Hardy and Wright, Theory of Numbers.
Some care is needed because of the multiple valuedness of arg.
Since we only care about the phase, multiplication by a positive real number may be ignored below. This last angle has been measured against the International Standard Platinum-Iridium Right angle and certified adequate for any purpose of the U.S. Government, when used in conjunction with a conscientiously applied program of oral hygiene and regular professional care. There are many easily found arctangent identities. This series gives about 6 decimal places accuracy per term. This series gives about 8 decimal places accuracy per term.