I made this nice model to address your problem and then remembered that my trial expired (still waiting on v3 to buy), so all I can give you is an image and a description.

Anyway, if I understand your question right, you want the cylinder to make a 15 degree angle projected onto the top view, and a 60 degree angle projected onto the front view. You're right that you can't do this with two rotations unless you do some math first to figure out the proper rotation angles. But, it can be done without math if you draw the cylinder last. First, draw lines in the top and front view with the desired angles. Then, extrude them both and get the intersection line between the two resulting surfaces. Next, create a c-plane aligned to this line, making sure that the z-axis is parallel to the intersection line. Finally, draw a circle on this c-plane and extrude it along the z-axis. Then you can cut it using a surface on the world x-y plane.

Hopefully that makes sense. In the attached image, the red lines and planes are the construction pieces I used to get the proper intersection line, and the gray plane is the cutting plane. Sorry I couldn't provide a 3dm file, and hopefully this is the kind of result you're shooting for.

Dan