One way would be like the following. Let us define the function `rule` as follows:
Clear[rule];
rule[expr_] :=
ReplaceAll[
expr, {Sin[2 \[Gamma]_] -> 2*Sin[\[Gamma]]*Cos[\[Gamma]],
Cos[2 \[Gamma]_] -> Cos[\[Gamma]]^2 - Sin[\[Gamma]]^2}];
and map this function on your expression. For the sake of shortness I take here only a small part of your otherwise a too long expression. The effect is, however, the same, I checked. So, let this:
expr=(Cos[Subscript[\[CapitalTheta], 12]] Sin[2 \[Gamma]] f[Subscript[r,
1], Subscript[r, 2], \[Alpha], \[Beta], \[Gamma],
Subscript[\[CapitalTheta], 12]])/(2 Sin[\[Beta]] Sin[
Subscript[\[CapitalTheta], 12]]^2
\!\(\*SubsuperscriptBox[\(r\), \(1\), \(2\)]\) Subscript[\[Mu], 1])
be your expression in the `StandardForm`. Then this
Map[rule, expr]//TraditionalForm
returning this:
(* (sin(\[Gamma]) cos(\[Gamma]) cos(Subscript[\[CapitalTheta], 12]) f(Subscript[r, 1],Subscript[r, 2],\[Alpha],\[Beta],\[Gamma],Subscript[\[CapitalTheta], 12]))/(Subscript[\[Mu], 1] Subsuperscript[r, 1, 2] sin(\[Beta]) sin(Subscript[\[CapitalTheta], 12])^2) *)
Though it looks awfully here, this: ![enter image description here][1]
is what you see on the screen. And suchlike looks each term.
[1]: https://i.sstatic.net/ZBkJP.jpg