Okay, so in the rest frame the angle of reflection will be equal to the angle of incidence? So sin(theta_in) = -cos(theta_iin)?
Which would give: P_in = (E/c)(sin(theta_in), -cos(theta_in), 0, 1)
And thus P(prime)_in = (E/c) ( (gamma)sine(theta)in - B), -cos(theta_in), 0, (gamma)(1-B))
And...