Circular Slice I

A random angle $\theta_1 \sim \text{Unif}(0, 2\pi)$ is selected. Then, the arc of the unit circle that sweeps out $\theta_1$ radians is marked red going counterclockwise starting from $(1, 0)$. Two other angles $\theta_2, \alpha \sim \text{Unif}(0, 2\pi)$ IID are also selected. Afterwards, an arc of length $\theta_2$ radians starting from the point that is $\alpha$ radians counterclockwise of $(1, 0)$ is swept out and colored blue. Find the probability that the blue and red regions are disjoint.