arctan x + arctan y = arctan (x+y / 1-xy)
arctan (x+y / 1-xy) + arctan z = arctan (x + y + z - xyz/ 1 - xy - zx - zy)
If tan pi = 0 , then the de numerator is also 0 , solve it and you will get it
tan pie/2 = infinity, denominator = 0 , solve it and you will get it
hope this helps