We discussed different angle set conventions in class. One common convention is the set of X-Y-Z Euler Angles. With this convention, the B frame is first rotated about  by angle , then rotated about  by angle , and then finally rotated about  by angle . This angle set has the following form.

^AR^B_{X' Y' Z'} ( \alpha, \beta, \gamma) =    \left[
         \begin{array}{ccc}
         c \beta c \gamma & - c \beta s \gamma & s \beta           \\
         s \alpha s \beta c \gamma + c \alpha s \gamma & - s \alpha s \beta s \gamma + c \alpha c \gamma & - s \alpha c \beta \\
         - c \alpha s \beta c \gamma + s \alpha s \gamma  & c \alpha s \beta s \gamma + s \alpha c \gamma & c \alpha c \beta
        \end{array}
    \right]

Using the examples from class as a primer, and using the atan2 function, please derive the formulas necessary to extract the values of angles , , and  from the above rotation matrix. For simplicity, you may assume that no angles equal either 0° or 90°. Please express your answers in terms of elements of the rotation matrix (, , etc.) and clearly state any assumptions that you make.