= Solution
<Momentum> conservation makes the sum of the two photon <momenta> parallel to $u$, so all three <vectors> are coplanar. Put the photons on opposite sides of the incident direction. Transverse and longitudinal <momentum> and energy conservation give
$$
E_1\sin\theta_1=E_2\sin\theta_2,
$$
$$
E_1\cos\theta_1+E_2\cos\theta_2=\gamma muc,
\qquad E_1+E_2=mc^2(\gamma+1).
$$
Eliminating $E_1,E_2$ yields
$$
\frac{\sin(\theta_1+\theta_2)}{\sin\theta_1+\sin\theta_2}
=\frac{\gamma u/c}{\gamma+1}
=\sqrt{\frac{\gamma-1}{\gamma+1}}.
$$
Using the half-angle identities on the left gives exactly
$$
\boxed{\frac{1+\cos(\theta_1+\theta_2)}{\cos\theta_1+\cos\theta_2}
=\sqrt{\frac{\gamma-1}{\gamma+1}}.}
$$
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