e^x - (e^x*1i)^-1i - (e^pi)*sin( x + [pi/2] ) and symbolic solve fully ?

Sorry, but it looks to me that you don't read or don't understand the answers you were given in other, similar threads!

I already told you, that you have a multi-valued expression and that

So basically you try to solve

and as usual Mathcad and its symbolics is of no help here.

You may graph some of the many possible functions (depending on parameter k) and find some numeric solutions for each

But Mathcads symbolics is of no use here, as it switches to float mode and returns only one specific solution out of an infinite number of possible solutions and as we know its also not possible to control (using assume) which one Mupad will pick.

The only case where Mathcad can provide all solutions is the trivial case with k=0 and its only this case which FM had shown in his contribution. But there are a lot more and for k!=0 we have an equation which is not algebraically solvable, so you will have to resort to numerical methods anyway.

All the above assumes that you are looking for real valued x. If x can/should be non-real, too, things will get a but more complex(!).

But honestly - (e^(x*i))^(-i) and your ignorance of the inability of Mathcad in dealing with it, is slowly becoming a little bit boring.