2012/029) find the value of arctan 1 + arctan 2 + arctan 3

tan (x+y + z) = (tan x + tan y + tan z - tan x tan y tan z)/(1- tan x tan y - tan y tan z - tan z tan x)

we see tan (arctan 1 + arctan 2 + arctan3) = 0

so arctan 1 + arctan 2 + tarctan 3 = n π ( we need to calculate n)

as each of arcran 1, arctan 2, artctan 3 are > 0 and < π /2 so sum > 0 and < 3 π /2

so n > 0 and < 3/2 and n is integer so n = 1

hence arctan 1 + arctan 2 + tarctan 3 = π