Complicated trigonometric functions prevent simplification

When appearing in an implicit frame, this does not allow the calculation to proceed:

<< EDCRGTCcode.m

xIN = {x, y, z, w}

gIN = DiagonalMatrix[{1, 1, 1, -1}]

d[coframe] with complicated dependence on trigonometric functions:

deList = {-Sec[2 w] Tan[w] e[1]⋀e[4] - 
          2 Sec[w] e[2]⋀e[3], 
        2 Tan[w] e[1]⋀e[3] + 
          (1/2) (-4 Csc[4 w] + Tan[w]) e[2]⋀e[
                4], -2 Cot[2 w] e[1]⋀e[2] + 
          (1/2) (Cot[w] + 2 Tan[w]) e[3]⋀e[4], 0}

dxRuleList = {d[w] -> e[4]}

simpRules = TrigRules;

The coframe basis is actually closed, but this cannot be verified with the predefined TrigRules:

FacSimp[d[deList] /. d[e[i_]] :> deList[[i]] /. 
        dxRuleList]

Simplify[%]

As a result RGtensors aborts the calculation:

RGtensors[gIN, xIN, {e[]}]

Solution: change coordinates to eliminate trigonometric functions: Cos[w]->t

Clear$dx

xIN={x,y,z,t}

simpRules = {}

deList=FacSimp[{-Sec[2 w] Tan[w] e[1]⋀e[4] - 
              2 Sec[w] e[2]⋀e[3], 
            2 Tan[w] e[1]⋀e[3] + 
              (1/2) (-4 Csc[4 w] + Tan[w]) e[2]⋀e[
                    4], -2 Cot[2 w] e[1]⋀e[2] + 
              (1/2) (Cot[w] + 2 Tan[w]) e[3]⋀e[4], 0}/.{Sec[w] -> 1/t, 
              Sec[2  w] -> 1/(2  t^2 - 1), 
              Tan[w] -> (Sqrt[1 - (t^2)])/t, 
              Cot[w] -> t/(Sqrt[1 - (t^2)]), 
              Cot[2  w] -> (2  t^2 - 1)/(2  t (Sqrt[ 1 - (t^2)])), 
              Csc[4  w] -> 
                1/(4  t (Sqrt[ 1 - (t^2)]) (2  t^2 - 1))}]

dxRuleList = {d[t] -> -(Sqrt[1 - (t^2)]) e[4]}

FacSimp[d[deList] /. d[e[i_]] :> deList[[i]] /. 
        dxRuleList]

RGtensors[gIN, xIN, {e[]}]

Rdd