The functions Rs and Rp become complex for \[Theta]0 = ArcSin[50/69]. You can insert that value into the integration interval as {\[Theta], 0, \[Theta]0, \[Pi]/2}, which silences the messages. You are using the symbol R with two different meanings, which may not be a good idea. The. I am afraid NIntegrate does not have a special notation.
