Is there an identity for $\arctan(x+y)$? Ive tried looking on the internet and I can't seem to find any identities for $\arctan(x+y)$. I was wondering if anyone knows any? 
Thanks!

$$\arctan(x+y) + \arctan(x-y) = \arctan\left(\frac{2 x}{1-x^2+y^2}\right) \tag 1 $$
is valid because take tan on both sides using
$$ \tan( x+y)=\frac{\tan x + \tan y}{1- \tan x \tan y} $$
(1) holds. Similarly
$$\arctan(x+y) - \arctan(x-y) = \arctan\left(\frac{2 y}{1+x^2-y^2}\right) \tag 2 $$
Taking sum
$$2 \arctan(x+y)  = \arctan\left(\frac{2 x}{1-x^2+y^2}\right)+\arctan\left(\frac{2 y}{1+x^2-y^2}\right)$$
If $z= x+iy  , u = $ real part of $ z^2 $
$$ 2 \arctan(x+y)  = \arctan\left(\frac{2 x}{1-u}\right)+\arctan\left(\frac{2 y}{1+u}\right)$$
for whatever use it could be put to..
