4. Given three planes $\alpha, \beta, \gamma$, the angle between each pair of planes is $\theta$, and $\alpha \cap \beta=a, \beta \cap \gamma=b, \gamma \cap \alpha=c$. If
Proposition A: $\theta>\frac{\pi}{3}$.
Proposition B: $a, b, c$ intersect at one point.
Then
(A) A is a sufficient condition for B but not necessary;
(B) A is a necessary condition for B but not sufficient;
(C) A is a necessary and sufficient condition for B;
(D) None of (A), (B), (C) is correct.
4. (A)

Let $a, b, c$ intersect at one point. From a point inside the trihedral angle, draw three rays perpendicular to $\alpha, \beta, \gamma$, respectively. The angle between each pair of these rays is $\pi-\varphi$, where $\varphi$ is the dihedral angle between the planes, and the sum is $3(\pi-\varphi)\frac{1}{3} \pi$. 
When $\varphi>\frac{2}{3} \pi$,
$$
\theta<\frac{1}{3} \pi \text {. }
$$

If $a, b, c$ do not intersect at one point, then they are mutually parallel, in which case $\varphi=\frac{1}{3} \pi$. Answer (A).
(Note: The range of the angle between two planes is $0<\theta \leqslant \frac{1}{2} \pi$)