Expected Distance on a Circle

Calculus Level 5

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

Let the expected value of PA+PB2PA+PB-2 be EE.

What is 1000E\lfloor 1000E\rfloor?

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