Angular relation for two-photon electron-positron annihilation ($\frac{1+\cos ({\theta }_1+{\theta }_2)}{\cos {\theta }_1+\cos {\theta }_2}=\sqrt{\frac{\gamma -1}{\gamma +1}}$)

When an electron of Lorentz factor $\gamma >1$ annihilates with a stationary equal-mass positron, transverse four-momentum conservation makes the photons' transverse components opposite. Eliminating their positive frequencies gives the displayed relation for noncollinear photon angles to the incoming electron. The exactly collinear forward/backward configuration is physically allowed but makes the quotient $0/0$; its undivided cross-multiplied identity remains valid. The angle relation thus requires nondegeneracy or an appropriate limit, rather than an assertion that every allowed angle pair defines the quotient.