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Initial Coordinate system (x,y,z) a rotation is desired about x lets say α=30 degrees so that a new coordinate system is formed (x',y',z') (This is simple part just using the matrix for rotation its straight forward). But it is not clear to me how another rotation lets say about y' (β=60) would be expressed to get the expression in the initial (x,y,z).

The expression R(α)*R(β) simple gives rotation about (x,y,z), but it is desired to rotated about y' in the second rotation.

Any insight would help.

My try always give me a minus sign away. I will post what i tried when i type it out.