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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 = Y * Z * X $

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

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

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

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

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

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

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

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

\begin{alignat*}{3}
\phi &= atan(\frac{ sin \phi }{ cos \phi }) &&= atan(\frac{ M_{c1,r2} }{ M_{c2,r2} }) \\
\theta &= 0 && = 0 \\
\psi &= asin(1) &&= \frac{\pi}{2} \\
\end{alignat*}

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

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

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

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

\begin{alignat*}{3}
\phi &= atan(\frac{ sin \phi }{ cos \phi }) &&= atan(\frac{ M_{c1,r2} }{ M_{c2,r2} }) \\
\theta &= 0 &&= 0 \\
\psi &= asin(-1) &&= -\frac{\pi}{2} \\
\end{alignat*}