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: is what you see on the screen. And suchlike looks each term.

One way would be like the following. Let us define the function rule as follows:

Clear[rule]; rule[expr_] := ReplaceAll[ expr, {Sin[2 γ_] -> 2*Sin[γ]*Cos[γ],   Cos[2 γ_] -> Cos[γ]^2 - Sin[γ]^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[Θ, 12]] Sin[2 γ] f[Subscript[r, 1], Subscript[r, 2], α, β, γ, Subscript[Θ, 12]])/(2 Sin[β] Sin[ Subscript[Θ, 12]]^2 \!\(\*SubsuperscriptBox[\(r\), \(1\), \(2\)]\) Subscript[μ, 1]) 

be your expression in the StandardForm. Then this

Map[rule, expr]//TraditionalForm 

returning this:

(* (sin(γ) cos(γ) cos(Subscript[Θ, 12]) f(Subscript[r, 1], Subscript[r, ],α,β,γ, Subscript[Θ, 12]) )/(Subscript[μ, 1] Subsuperscript[r, 1, 2] sin(β)  sin(Subscript[Θ, 12])^2) *) 

Though it looks awfully here, this:

is what you see on the screen. And suchlike looks each term.