I have two coordinates. One is standard and the other is arbitrary.
A rotation is represented as ZYX in the standard coordinates. (yes, It is not exactly a Euler angle. I'm sorry about this) and alpha, beta, gamma are angles of each corresponding axis.
If arbitrary coordinates are given and each basis are known, Can I calculate each angle of new basis?
I'm not a good hand-writer but I added an image for explanation. Thank you for your help