About coordinate angle computing

Dear Firend: There has two Space rectangular coordinate， and the angle between each corresponding axis is konwn,( for example: the angle between x and x'defined as alpha, y and y'defined as beta, z and z'defined as gamma). Cound I get the RPY angle which can transfer one coordinate to another? (the RPY angle are rotate obey the squence as follow: roll from z axis ,pitch from the Y axis and yaw from the x axis). Thanks ahead!