= Solution
By <four-momentum conservation>, $p_\pi=p_1+p_2$. With the $(-,+,+,+)$ <Minkowski metric>, the <neutral pion> has $p_\pi^2=-M_\pi^2$, while each <photon> has $p_i^2=0$ and $|\mathbf p_i|=E_i$. Taking the <Minkowski norm> gives
$$
-M_\pi^2=2p_1\cdot p_2
=2(-E_1E_2+\mathbf p_1\cdot\mathbf p_2)
=-2E_1E_2(1-\cos A).
$$
The half-angle identity therefore yields
$$
\boxed{\sin^2(A/2)=\frac{M_\pi^2}{4E_1E_2}.}
$$
This is a measurement of the <diphoton invariant mass> using two <photon> <energies> and their opening angle, independent of the <neutral pion>'s laboratory <velocity>.
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