2. (1990 First "Hope Cup" Invitational Competition Reserve Question) Given $x, y, z \in (0, +\infty)$, and $\frac{x^{2}}{1+x^{2}}+\frac{y^{2}}{1+y^{2}}+$ $\frac{z^{2}}{1+z^{2}}=2$, find the maximum value of $\frac{x}{1+x^{2}}+\frac{y}{1+y^{2}}+\frac{z}{1+z^{2}}$.