Given the function $f ( x ) = \left( \frac { 1 } { x } + a \right) \ln ( 1 + x )$.\\
(1) When $a = - 1$, find the equation of the tangent line to the curve $y = f ( x )$ at the point $( 1 , f ( 1 ) )$.\\
(2) Do there exist $a$ and $b$ such that the curve $y = f \left( \frac { 1 } { x } \right)$ is symmetric about the line $x = b$? If they exist, find the values of $a$ and $b$. If they do not exist, explain why.\\
(3) If $f ( x )$ has an extremum on $( 0 , + \infty )$, find the range of $a$.