[ \normalsize}} \frac{\gamma_{3}}{\gamma_{1}} U_{1}( \gamma_{1}, \gamma_{2}, \gamma_{3}, 0)  \; -\;U_{3}( \gamma_{1}, \gamma_{2}, \gamma_{3}, 0 ) {\mbox{\large ] \normalsize}}
\quad\end{aligned}$$

$$\label{eqn149a}
\gamma_{1} U_{1}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta ) \;+\; \gamma_{2}\, U_{2}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta ) \;+\; \gamma_{3}\, U_{3}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta ) \;=\;0$$

Determinant of this system is

$$\begin{aligned}
\label{eqn1481b}
\Delta = \left| \begin{array}{ccc}
{\mbox{\large [ \normalsize}}\eta \;+\;\nu( \gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2}){\mbox{\large ] \normalsize}}\frac{\gamma_{2}}{\gamma_{1}} & -{\mbox{\large [ \normalsize}}\eta \;+\;\nu( \gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2}){\mbox{\large ] \normalsize}} & 0 \\
\nonumber\\
 {\mbox{\large [ \normalsize}}\eta \;+\;\nu( \gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2}){\mbox{\large ] \normalsize}}\frac{\gamma_{3}}{\gamma_{1}} & 0 & -{\mbox{\large [ \normalsize}}\eta \;+\;\nu( \gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2}){\mbox{\large ] \normalsize}} \\
\nonumber\\ 
\gamma_{1} & \gamma_{2} & \gamma_{3} \end{array} \right| = 
\nonumber\\ 
\nonumber\\
\nonumber\\
=\;\frac{{\mbox{\large [ \normalsize}}\eta \;+\;\nu( \gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2}){\mbox{\large ] \normalsize}}^{2}( \gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2})}{\gamma_{1}}
\neq \;\; 0
\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\end{aligned}$$

And consequently the system of equations $(\ref{eqn147})\;-\; (\ref{eqn149})\;$ and/or $\;(\ref{eqn147a})\;-\; (\ref{eqn149a})\;$ has a unique solution. Taking into account formulas $(\ref{eqn150})\;-\; (\ref{eqn152})\;$ we can write this solution in the following form:

$$\begin{aligned}
\label{eqn153}
U_{1}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta )\;=\;\frac{[( \gamma_{2}^{2} +\gamma_{3}^{2})  \tilde{F}_{1}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta) - \gamma_{1}\gamma_{2} \tilde{F}_{2}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta) - \gamma_{1}\gamma_{3} \tilde{F}_{3}^{\otimes}( \gamma_{1}, \gamma_{2}, \gamma_{3}, \eta)]}{ (\gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2}) [\eta+\nu (\gamma_{1}^{2} +\gamma_{2}^{2} +\gamma_{3}^{2})] }\;+\nonumber
\\
\nonumber\\
+\; \frac{ U_{1}^{0}(\gamma_{1} 