  In 2002, two neutrino mixing ansatze having trimaximally-mixed middle
($\nu_2$) columns, namely tri-chi-maximal mixing ($\text{T}\chi\text{M}$) and
tri-phi-maximal mixing ($\text{T}\phi\text{M}$), were proposed. In 2012, it was
shown that $\text{T}\chi\text{M}$ with $\chi=\pm \frac{\pi}{16}$ as well as
$\text{T}\phi\text{M}$ with $\phi = \pm \frac{\pi}{16}$ leads to the solution,
$\sin^2 \theta_{13} = \frac{2}{3} \sin^2 \frac{\pi}{16}$, consistent with the
latest measurements of the reactor mixing angle, $\theta_{13}$. To obtain
$\text{T}\chi\text{M}_{(\chi=\pm \frac{\pi}{16})}$ and
$\text{T}\phi\text{M}_{(\phi=\pm \frac{\pi}{16})}$, the type~I see-saw
framework with fully constrained Majorana neutrino mass matrices was utilised.
These mass matrices also resulted in the neutrino mass ratios,
$m_1:m_2:m_3=\frac{\left(2+\sqrt{2}\right)}{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left(2+\sqrt{2}\right)}{-1+\sqrt{2(2+\sqrt{2})}}$.
In this paper we construct a flavour model based on the discrete group
$\Sigma(72\times 3)$ and obtain the aforementioned results. A Majorana neutrino
mass matrix (a symmetric $3\times 3$ matrix with 6 complex degrees of freedom)
is conveniently mapped into a flavon field transforming as the complex 6
dimensional representation of $\Sigma(72\times 3)$. Specific vacuum alignments
of the flavons are used to arrive at the desired mass matrices.
