How Is the Maximum Energy Transfer Determined in a Photon-Electron Collision?

[Quelsita]

A photon of initial energy E_i=2.4E3 eV collides with a free electron, initially stationary. What is the maximum energy that the electron can acquire in this collision?

-we know that conservation of energy requires that the Kinetic energy of the eletron gained must equal that lost by the photon so
(delta)E_photon=(delta)E_electron

I considered finding the final energy using
(delta)lambda=(h/m_ec)(1-cos(theta)) where =(h/m_ec) is the compton wavelength=0.02426A
which can be rearranged
hc/(delta)E=(0.02426A)(1-cos(theta))

My question is, how do we find the final energy of the photon without knowing the angle of deflection? Or can we assume that the electron and photon both move in opposite directions?

Thanks!

 

[Quelsita]

OK, I just read over another problem which specifically mentions symmetric scattering so I'm assuming that is not the case here.