Well - I found a way how to achieve my goal ...
My main issue was that I was not able to good sketch.
Here's my way to find the rotation angle ...
I have got the following details available:
length blue line (= length)
Angle between red and yellow line (= A)
Angle between grey and blue line (= B = 90 - A)
Angle between the pink continous lines (= C)
To search: Angle between grey and brown line (= X)
First I calculate the length of the grey line: length / COS(90 - C) (= length grey)
Next I calculate the length of the red line (between the intersection points with the yellow and the lightblue lines): length grey * SIN(90 - C) (= length red)
Now the length of the lightblue line: length red * SIN(A) (= length lightblue)
And now it's possible to calculate the angle X: ARCSIN(length lightblue / length grey)
It's really simple in the end - as soon as you have got a useful sketch ...
