  We develop the formalism based on the S-matrix for $3 \to 3$ scattering to
derive the direct three-body resonant radiative capture reaction rate. Within
this formalism the states, which decay only/predominantly directly into
three-body continuum, should also be included in the capture rate calculations.
%The results obtained indicate that some theoretical calculations are
%incomplete. Basing on the derivation, as well as on the modern experimental
data and theoretical calculations concerning $^{17}$Ne nucleus, we
significantly update the reaction rate for $^{15}$O($2p$,$\gamma$)$^{17}$Ne
process in explosive environment. We also discuss possible implementations for
the $^{18}$Ne($2p$,$\gamma$)$^{20}$Mg, $^{38}$Ca($2p$,$\gamma$)$^{40}$Ti, and
$^4$He($n\alpha$,$\gamma$)$^{9}$Be reactions.
