tan^(-1)(x) + tan^(-1)(y) = tan^(-1)$\frac{(x+y}{(1-xy)}$) ONLY when xy < 1. When xy > 1 and x,y > 0: add pi. When xy > 1 and x,y < 0: subtract pi. The JEE exploits this condition heavily. Example: tan^(-1)(2) + tan^(-1)(3): here xy = 6 > 1, both positive, so answer = pi + tan^(-1)(-1) = pi - pi/4 = 3*pi/4.