Hi Claude. you have to express the two points in quaestion in spherical coordinates.

Show[{SphericalPlot3D[
   Sin[Theta]*f[Theta, Phi] /. {a -> 1, b -> 1, c -> 1}, {Theta, 0, 
    Pi}, {Phi, 0, 2 Pi}, 
   PlotStyle -> Directive[Cyan, Opacity[0.3], Specularity[White, 10]],
    Mesh -> None, PlotPoints -> 300, 
   AxesLabel -> {Style["f", Bold, 15], 
     Style["\[CapitalTheta]", Bold, 15], Style["\[Phi]", Bold, 15]}, 
   PlotRange -> All, AspectRatio -> Automatic, ImageSize -> Large], 
  Graphics3D[{PointSize[Large], Black, 
    Point[({Sin[Theta] Cos[Phi], Sin[Theta] Sin[Phi], 
         Cos[Theta] f[Theta, Phi]} /. {a -> 1, b -> 1, c -> 1}) /. 
      Last@N[LeMin]]}], 
  Graphics3D[{PointSize[Large], Red, 
    Point[({Sin[Theta] Cos[Phi], Sin[Theta] Sin[Phi], 
         Cos[Theta] f[Theta, Phi]} /. {a -> 1, b -> 1, c -> 1}) /. 
      Last@N[ LeMax]]}]}]

Regards Roland