Comparing a Triangle and a Sector of a Circle Two wood sticks and a metal rod, each of length $1,$ are connected to form a triangle with angle $\theta_{1}$ at the point $P$ , as shown in the first figure below. The rod is then bent to form an arc of a circle with center $P$ , resulting in a smaller angle $\theta_{2}$ at the point $P$ as shown in the second figure. Find $\theta_{1}, \theta_{2},$ and $\theta_{1}-\theta_{2}$