Propose a system with 3 sequential turns to go from an original Cartesian coordinate system (no prime) to a transformed

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Propose a system with 3 sequential turns to go from an original
Cartesian coordinate system (no prime) to a transformed system
(triple prime in this case) by turning about the axes. For each
twist, draw the axes and angles of twist involved, as well
as the tables of direction cosines. Check that the resulting
rotation is an orthogonal matrix.
NOTES:
-Each turn starts from the previous turn on its axis
-Each row and each column of the matrices must comply with the unit
vector property where their elements squared and added are =1,
since they are unit axes orthogonal to each other.
-The identification of the axes is xi'=first turn, xi''=second
turn, xi'''=third turn. The index i takes the values of 1,2,3; so
each unitary axis will have 3 components.
-Finally the multiplication of the matrices: [3rd turn]x[2nd
turn]x[1st turn] =[resulting direction cosine table]