3. Given that the domain of the function $f(x)$ is $(-1,1)$, for any $x, y \in(-1,1)$ we have
$$
\begin{array}{l}
f(x)+f(y)=f\left(\frac{x+y}{1+x y}\right) . \\
\text { If } f\left(\frac{a+b}{1+a b}\right)=1, f\left(\frac{a-b}{1-a b}\right)=2, \text { and }|a|<1,
\end{array}
$$
$|b|<1$, find the values of $f(a)$ and $f(b)$.
$$
\left\{\begin{array}{l}
f(a)+f(b)=1, \\
f(a)+f(-b)=2 .
\end{array}\right.
$$

The above text translated into English, retaining the original text's line breaks and format, is as follows:

$$
\left\{\begin{array}{l}
f(a)+f(b)=1, \\
f(a)+f(-b)=2 .
\end{array}\right.
$$

Note: The equations themselves are already in a universal format and do not require translation. The prompt and note are provided in English for clarity.