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$ X = \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & cos \phi & -sin \phi \\
0 & sin \phi & cos \phi \\
\end{array} \right) $

$ Y = \left( \begin{array}{ccc}
cos \theta & 0 & sin \theta \\
0 & 1 & 0 \\
-sin \theta & 0 & cos \theta \\
\end{array} \right) $

$ Z = \left( \begin{array}{ccc}
cos \psi & -sin \psi & 0 \\
sin \psi & cos \psi & 0 \\
0 & 0 & 1 \\
\end{array} \right) $


$ M = Z * X * Y $

M=\left( \begin{array}{ccc}
cos \psi & -sin \psi & 0 \\
sin \psi & cos \psi & 0 \\
0 & 0 & 1 \\
\end{array} \right) \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & cos \phi & -sin \phi \\
0 & sin \phi & cos \phi \\
\end{array} \right) \left( \begin{array}{ccc}
cos \theta & 0 & sin \theta \\
0 & 1 & 0 \\
-sin \theta & 0 & cos \theta \\
\end{array} \right) $

M=\left( \begin{array}{ccc}
cos \psi & -sin \psi & 0 \\
sin \psi & cos \psi & 0 \\
0 & 0 & 1 \\
\end{array} \right) \left( \begin{array}{ccc}
cos \theta & 0 & sin \theta \\
sin \phi sin \theta & cos \phi & -sin \phi cos \theta \\
-cos \phi sin \theta & sin \phi & cos \phi cos \theta \\
\end{array} \right) $

M=\left( \begin{array}{ccc}
cos \psi cos \theta - sin \psi sin \phi sin \theta &
-sin \psi cos \phi &
cos \psi sin \theta + sin \psi sin \phi cos \theta \\
sin \psi cos \theta + cos \psi sin \phi sin \theta &
cos \psi cos \phi &
sin \psi sin \theta - cos \psi sin \phi cos \theta \\
-cos \phi sin \theta &
sin \phi &
cos \phi cos \theta \\
\end{array} \right)$

\begin{alignat*}{3}
\phi &= asin(sin \phi) &&= asin(M_{c1,r2})\\
\theta &= atan(\frac{sin \theta}{cos \theta }) &&= atan(\frac{-M_{c0,r2}}{M_{c2,r2}})\\
\psi &= atan(\frac{sin \psi}{cos \psi}) &&= atan(\frac{-M_{c1,r0}}{M_{c1,r1}})\\
\end{alignat*}

\begin{flalign*}
sin \phi &= 1 \\
cos \phi &= 0 \\
\end{flalign*}

M=\left( \begin{array}{ccc}
cos \psi cos \theta - sin \psi sin \theta &
0 &
cos \psi sin \theta + sin \psi cos \theta \\
sin \psi cos \theta + cos \psi sin \theta &
0 &
sin \psi sin \theta - cos \psi cos \theta \\
0 &
1 &
0 \\
\end{array} \right)$

\begin{flalign*}
sin (\theta + \psi) &= cos \psi sin \theta + sin \psi cos \theta \\
cos (\theta + \psi) &= cos \psi cos \theta - sin \psi sin \theta \\
\end{flalign*}

M=\left( \begin{array}{ccc}
cos(\theta + \psi) & 0 &  sin(\theta + \psi) \\
sin(\theta + \psi) & 0 & -cos(\theta + \psi) \\
0 & 1 & 0 \\
\end{array} \right)$

\begin{alignat*}{3}
\phi &= asin(1) &&= \frac{\pi}{2} \\
\theta &= atan(\frac{sin \theta}{cos \theta}) &&= atan(\frac{M_{c2,r0}}{M_{c0,r0}}) \\
\psi &= 0 &&= 0 \\
\end{alignat*}

\begin{flalign*}
sin \phi &= -1 \\
cos \phi &= 0 \\
\end{flalign*}

M=\left( \begin{array}{ccc}
cos \psi cos \theta + sin \psi sin \theta &
0 &
cos \psi sin \theta - sin \psi cos \theta \\
sin \psi cos \theta - cos \psi sin \theta &
0 &
sin \psi sin \theta + cos \psi cos \theta \\
0 &
-1 &
0 \\
\end{array} \right)$

\begin{flalign*}
sin (\theta - \psi) &= cos \psi sin \theta - sin \psi cos \theta \\
cos (\theta - \psi) &= cos \psi cos \theta + sin \psi sin \theta \\
\end{flalign*}

M=\left( \begin{array}{ccc}
cos(\theta - \psi) & 0 & sin(\theta - \psi) \\
-sin(\theta - \psi) & 0 & cos(\theta - \psi) \\
0 & -1 & 0 \\
\end{array} \right)$

\begin{alignat*}{3}
\phi &= asin(-1) &&= -\frac{\pi}{2} \\
\theta &= atan(\frac{sin \theta}{cos \theta}) &&= atan(\frac{M_{c2,r0}}{M_{c0,r0}}) \\
\psi &= 0 &&= 0 \\
\end{alignat*}