(3) Given that the function $y=f(x)$ is an odd function on $\mathbf{R}$, and when $x \leqslant 0$, $f(x)=\frac{3^{x}}{9^{x}+1}-\frac{1}{2}$.
(1) Determine and prove the monotonicity of $y=f(x)$ on $(-\infty, 0)$;
(2) Find the range of $y=f(x)$;
(3) Solve the inequality $f(x)>\frac{1}{3}$.
(3) (1) Monotonically increasing on $(-\infty, 0)$
(2) $\left(-\frac{1}{2}, \frac{1}{2}\right)$
(3) $\left(\log _{3}(3+2 \sqrt{2}),+\infty\right)$