What is the best optimization method for the following function?

I have calculated the energy of the electrons as a function of their angles. and I want to find the angles for which my function (energy) is minimized. I have used NMinimize, but the angles I get from it doesn’t seem to be right as I expect a smooth change in the angles (My expectation may be wrong but I want to make sure that the problem is not coding or in other words the minimum is the Global minimum).

I have used Monte Carlo as well (I can post that if necessary but it doesn’t find the global at all so I thought may be it’s not the best way of optimization in this case). My first question is how to make sure the minimum energy I get is the Global minimum?

The second question is if you know any other better way to minimize my function so that I am sure the answer is the Global Min?

I post the code here (the angle for the first electron should be 0 and the last one should ne pi/2, so I fixed those in the begining):

 Clear["Global`*"]
 g[[ScriptL]0_Integer?NonNegative] := 
 g[[ScriptL]0] = 
 Module[{ne = 2 [ScriptL]0 + 2, vars, cons, [Gamma], factorFxn, 
 ene}, vars = Array[Symbol["x$" <> ToString[#]] &, ne];
 vars[[1]] = 0;
 vars[[ne]] = [Pi]/2;
 cons = Apply[And, Thread[0 <= vars[[2 ;; ne - 1]] <= [Pi]/2]];
 [Gamma] = 
 Join[Table[{Riffle[Range[0, -[ScriptL]0, -1], 
     Range[[ScriptL]0]][[i]], 1}, {i, 1, 2 [ScriptL]0 + 1}], 
 Table[{Riffle[Range[0, -[ScriptL]0, -1], 
     Range[[ScriptL]0]][[i]], -1}, {i, 1, 2 [ScriptL]0 + 1}]];

   factorFxn[[ScriptL]_, m1_, m2_, p1_, p2_] := 
   (If[[Gamma][[m1, 2]] == [Gamma][[p1, 2]] && [Gamma][[m2, 
      2]] == [Gamma][[p2, 2]],
    If[[Gamma][[p1, 1]] - [Gamma][[m1, 1]] == [Gamma][[m2, 
       1]] - [Gamma][[p2, 1]], 
    Sum[(2 [ScriptL] + 1)^2 Sum[
       If[[Gamma][[p1, 1]] - [Gamma][[m1, 1]] == 
          mval && [Gamma][[m2, 1]] - [Gamma][[p2, 1]] == 
          mval, (-1)^([Gamma][[m1, 1]] + [Gamma][[m2, 1]] + 
            
            mval) ThreeJSymbol[{[ScriptL], -[Gamma][[m1, 
             1]]}, {[ScriptL], [Gamma][[p1, 
            1]]}, {[ScriptL]temp, -mval}] ThreeJSymbol[{
      [ScriptL]temp, 
           mval}, {[ScriptL], -[Gamma][[m2, 
             1]]}, {[ScriptL], [Gamma][[p2, 
            1]]}] ThreeJSymbol[{[ScriptL], 0}, {[ScriptL], 
           0}, {[ScriptL]temp, 0}]^2, 
        0], {mval, -[ScriptL]temp, [ScriptL]temp}], 
   {[ScriptL]temp, 0, 2 [ScriptL]}], 0]
    , 0] -
    If[[Gamma][[m1, 2]] == [Gamma][[p2, 2]] && [Gamma][[m2, 
      2]] == [Gamma][[p1, 2]], 
    If[-[Gamma][[p1, 1]] + [Gamma][[m2, 
       1]] == -[Gamma][[m1, 1]] + [Gamma][[p2, 1]], 
    Sum[(2 [ScriptL] + 1)^2 Sum[
       If[-[Gamma][[p1, 1]] + [Gamma][[m2, 1]] == 
          mval && -[Gamma][[m1, 1]] + [Gamma][[p2, 1]] == 
          mval, (-1)^([Gamma][[m1, 1]] + [Gamma][[m2, 1]] + 
            mval) ThreeJSymbol[{[ScriptL], -[Gamma][[m1, 
             1]]}, {[ScriptL], [Gamma][[p2, 
            1]]}, {[ScriptL]temp, -mval}] ThreeJSymbol[{
   [ScriptL]temp, 
           mval}, {[ScriptL], -[Gamma][[m2, 
             1]]}, {[ScriptL], [Gamma][[p1, 
            1]]}] ThreeJSymbol[{[ScriptL], 0}, {[ScriptL], 
           0}, {[ScriptL]temp, 0}]^2, 
        0], {mval, -[ScriptL]temp, [ScriptL]temp}], 
  {[ScriptL]temp, 0, 2 [ScriptL]}], 0]
   , 0] );

  
      ene[th1_?VectorQ] :=(*(2 [ScriptL]0 +1)^2*) Sum[
    (* Find out which states we're calculating the matrix element of 
      *)
    (Cos[th1[[m2]]] Cos[th1[[m1]]] + 
    Cos[th1[[m2]]] Sin[th1[[m1 + 1]]] + 
    Cos[th1[[m1]]] Sin[th1[[m2 + 1]]] + 
    Sin[th1[[m2 + 1]]] Sin[th1[[m1 + 1]]] + 
    If[m1 == m2, Cos[th1[[m1]]] Sin[th1[[m2 + 1]]], 
     0])*(Cos[th1[[p2]]] Cos[th1[[p1]]] + 
    Cos[th1[[p2]]] Sin[th1[[p1 + 1]]] + 
    Cos[th1[[p1]]] Sin[th1[[p2 + 1]]] + 
    Sin[th1[[p2 + 1]]] Sin[th1[[p1 + 1]]] + 
    If[p1 == p2, Cos[th1[[p1]]] Sin[th1[[p1 + 1]]], 
     0]) factorFxn[[ScriptL]0, m1, m2, p1, p2]
 
    , {p1, 1, 2 [ScriptL]0 + 1}, {m1, 1, 2 [ScriptL]0 + 1}, {p2, 1,
    p1}, {m2, 1, m1}]; {ne, #} & /@ 
   NMinimize[{ene[vars], cons}, vars[[2 ;; ne - 1]], 
   Method -> "SimulatedAnnealing"]]

I would appreciate any suggestions to go about this.