4. Given that $a, b, c$ are the lengths of the three sides of $\triangle ABC$, and satisfy the conditions
$$
\frac{2 a^{2}}{1+a^{2}}=b, \frac{2 b^{2}}{1+b^{2}}=c, \frac{2 c^{2}}{1+c^{2}}=a \text {. }
$$

Then the area of $\triangle ABC$ is . $\qquad$