$12\mathrm{.}29.$ Decay into photons $*$

A mass $m$ moving at speed $v$ decays into two photons. One photon moves perpendicular to the original direction, and the other photon moves off at an angle $,$ as shown in Fig. $12\mathrm{.}26.$ Show that if $tan=\frac{1}{2},$ then $\frac{v}{c}=\frac{\sqrt[\phantom{2}]{5}-1}{2},$ which just happens to be the inverse of the golden ratio.