Question 155
Let $a$ and $b$ be real numbers which satisfy the equality $\frac{a^2}{1+a^2} + \frac{b^2}{1+b^2} = 1$. Determine all possible values of the expression
$$
(a + b) \left( \frac{a}{1 + a^2} + \frac{b}{1 + b^2} \right).
$$
$$
(a + b) \left( \frac{a}{1 + a^2} + \frac{b}{1 + b^2} \right).
$$