Consider a vector in 3D. Its projections on two planes, say YX and YZ planes, makes some angle with the vertical axis ( the y axis in this case). I know these two angles (I call them projected angles). This is the only information I have about the vector. I need Euler angles which when applied on a unit vector in vertical direction will rotate the unit vector in the direction of the original vector. Practical application: This would be used to assess angular deformities in tibia/femur. Surgeons know about these projected angles through x-rays in AP and ML planes ( equivalent to YX and YZ planes above). I need to convert them to Euler angles for my application.