A photon with an initial wavelength \(\lambda_0\) collides with an electron that is initially at rest. As a result of the Compton scattering process, the recoiling electron receives a kinetic energy equal to exactly half of the initial energy of the incident photon. In terms of \(\lambda_0\), electron mass \(m_e\), speed of light \(c\), and Planck's constant \(h\), which of the following expressions correctly gives the cosine of the photon's scattering angle, \(\cos\theta\)?