Fresnel Simplification

I poorly attempted to simplify the complex Fresnel equation to see if we could use it like the Schlick’s approximation and decompose the FGD integral computation into 2 parts, but this time with the guarantee that FGD = 0 when (Subscript[F, 0])=0 (i.e. IOR=1)...

fresnel=Function[{c,F0},
ior=((1+(Sqrt[F0]))/(Max[0.0001,1-(Sqrt[F0])]));
g=(Sqrt[(ior^2)-1+(c^2)]);
a = c*(g-c);
b=c*(g+c);
F=(1/2)((a^2)/(b^2))(1+((((b-1))^2)/(((a+1))^2)));
F
];
fresnel[Cos[1.57],0.04]

Manipulate[Plot[fresnel[Cos[θ],F0],{θ,0,(π/2)},PlotRange->{0,1}],{F0,0,1}]

fresnel2=Function[{c,F0},
ior=((1+(Sqrt[F0]))/(Max[0.0001,1-(Sqrt[F0])]));
g=(Sqrt[(ior^2)-1+(c^2)]);
a = c*(g-c);
b=c*(g+c);
F=(1/2)((((a+1))^2)/(((b+1))^2))(1+((((b-1))^2)/(((a+1))^2)));
F
];
fresnel2[Cos[1.57],0.04]

Manipulate[Plot[fresnel2[Cos[θ],F0],{θ,0,(π/2)},PlotRange->{0,10}],{F0,0,1}]