15. The quadratic function $f(x)=a x^{2}+b x+c(a, b, c \in \mathbf{R}, a \neq 0)$ satisfies the following conditions:
(1) $f(-1)=0$;
(2) For $x \in \mathbf{R}$, $f(x) \geqslant x$;
(3) For $x \in(0,2)$, $f(x) \leqslant \frac{(x+1)^{2}}{4}$.
If $x_{1}, x_{2}, x_{3} \in(0,2)$, and $\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}=3$, find the minimum value of $f\left(x_{1}\right) f\left(x_{2}\right) f\left(x_{3}\right)$.