3. Let $a, b, c \in \mathbf{R}_{+}$, and $a+b+c=1$. Find
$$
\frac{3 a^{2}-a}{1+a^{2}}+\frac{3 b^{2}-b}{1+b^{2}}+\frac{3 c^{2}-c}{1+c^{2}}
$$

the minimum value.
( Hint: First prove $\frac{3 a^{2}-a}{1+a^{2}} \geqslant \frac{9}{10}\left(a-\frac{1}{3}\right)$. Similarly, obtain the other two inequalities. Then add the three inequalities, to get the minimum value of 0. )