1986 AMC 12 Question 21

In the configuration below, $\theta$ is measured in radians, $C$ is the center of the circle, $BCD$ and $ACE$ are line segments, and $AB$ is tangent to the circle at $A.$



A necessary and sufficient condition for the equality of the two shaded areas, given $0\lt\theta\lt\frac{\pi}{2},$ is