Expected Distance on a Circle

Calculus Level 5

An angle $\theta$ is chosen randomly in the interval $[0,2\pi )$ , and its corresponding point on the unit circle is plotted. Let this point be $P$ . Now let $A=(1,0)$ and $B=(-1,0)$ .

Let the expected value of $PA+PB-2$ be $E$ .

What is $\lfloor 1000E\rfloor$ ?