4.94 Solve the equation $\operatorname{arctg} x+\operatorname{arctg}(1-x)=2 \operatorname{arctg} \sqrt{x-x^{2}}$.
[Solution] $\because x(1-x) \geqslant 0, \therefore \quad x \in[0,1]$ and $x(1-x) \leqslant \frac{1}{4}$. Taking the tangent on both sides of the equation, we get
$$\frac{x+(1-x)}{1-x(1-x)}=\frac{2 \sqrt{x(1-x)}}{1-x(1-x)}$$

Since $x(1-x) \neq 1$, we get the equation
$$\sqrt{x(1-x)}=\frac{1}{2}$$

This yields $x=\frac{1}{2}$.