Sumation of arctangent

If $x,y,z\in R$ prove that $\arctan x+ \arctan y+\arctan z=\arctan {\frac{s_1-s_3}{1-s_2}}$ where
$s_1=x+y+z,s_2=xy+yz+zx,s_3=xyz$
More generally $\arctan x_1+...+\arctan x_n=$
$