I don't think your looking to "unwrap a curve". Essentially, that's just the length of the entity. You wont really have "2 angles". Cutting a pipe at an angle will essentially just be an ellipse, correct? So you would have a single angle cut, then rotate the part on it's axis to get the other angle.
There's probably some complex math formula to get the angle of the cut, but here's how I would do it. Use a solid cylinder and rotate it by the 2 values you have (60 degree's to the side then 15 forward)
Now Boolean diff the cylinder with a plane and delete half of it. Now set and rotate the cut cylinder so it is sitting flat and perp in the x and y planes again. This will give you a simple angle cut to make on a pipe.
Now setting it flat on that cut will give "some" angle to the pipe. Rotating/pivoting it's placement will generate the 60/15 angle you want... the welder will be responsible for the exact degree...
Here's an iges file: