Hi Rudl  sometimes it can be helpful to create some vertical circles that can then be intersected to find the precise amount to rotate around an axis to align to some other geometry.
If you've got 2 circles they will generate an intersection snap point where they meet, and if you want to snap to the intersection between a circle and a surface you can select the surface and the circle and run the Construct > Curve > Isect command to generate a point object where they intersect each other and then that point can be snapped on to.
See this previous post for an example:
http://moi3d.com/forum/index.php?webtag=MOI&msg=2140.46
There 2 flat profiles are rotated by the precise amount to have their points touching by creating 2 vertical circles and snapping on to their intersection. The vertical circles are created perpendicular to the rotation axis that will be used for rotating each shape.
However, I'm not entirely certain if that applies to what you are asking for because that kind of thing involves rotating a shape around a axis, and a rotation axis is a line. In your picture you seem to almost be indicating a curved segment of the curve as the rotation axis? But rotation does not naturally occur around a curved segment like that, a normal kind of rotation happens around a straight line axis...
 Michael
