= Solution
For $0<T\ll Mc^2$, the ratio in <9> tends to $1/2$, giving
$$
\boxed{\theta\longrightarrow45^\circ,\qquad 2\theta\longrightarrow90^\circ.}
$$
This recovers the nonrelativistic equal-mass <elastic collision> result: <momentum conservation> gives $\mathbf v_i=\mathbf v_1+\mathbf v_2$, while conservation of <kinetic energy> gives $v_i^2=v_1^2+v_2^2$. Subtracting the squared momentum relation leaves $\mathbf v_1\cdot\mathbf v_2=0$. Exactly at $T=0$ there are no outgoing nonzero velocities defining such angles; the result is the limit through positive <kinetic energies>.
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