solve for x : inv(x) = val

solve_inv.bas

Function inv(x As Double) As Double
    ' Define involute function
    inv = Tan(x) - x
End Function

Function solve_inv(val As Double) As Double
    ' Solve for x : inv(x) = val
    Dim x0 As Double, x1 As Double
    Dim eps As Double, pi As Double
    
    eps = 0.00001
    pi = 4# * Atn(1#)
    
    x1 = pi / 4#
    
    Do
        x0 = x1
        x1 = x0 - (inv(x0) - val) / Tan(x0) ^ 2
    Loop While Abs(x1 - x0) > eps
    
    solve_inv = x1 'radian
End Function