=0$, $\varphi_1 =0$, $\vartheta^{\prime}_{1}=\pi/2$, $\varphi^{\prime}_{1}=0$, $\vartheta_2 =\pi/4$, $\varphi_2 =0$, $\vartheta^{\prime}_{2}=-\pi/4$, and $\varphi^{\prime}_{2}=0$. Substituting these values (together with $c_1 = -c_2 = 1/\sqrt{2}$, $\vartheta_3 =\pi/2$, $\varphi_3 =0$, $\gamma =-1$, and $z_3 =+1$) into the left-hand side of inequality (13) gives the maximum violation $2\sqrt{2}$. Since the unit vector ${\bf{\text n}}$ is quite arbitrary, we conclude that there are infinitely many sets of directions $\vec{e}_1$, $\vec{e}\,^{\prime}_{1}$, $\vec{e}_2$, and $\vec{e}\,^{\prime}_{2}$ satisfying the equality $$\begin{aligned}
|&& \cos \vartheta_1 \cos\vartheta_2 + \cos\vartheta_1 
\cos\vartheta^{\prime}_{2} + \cos\vartheta^{\prime}_{1} \cos\vartheta_2  \nonumber  \\
&& - \cos\vartheta^{\prime}_{1} \cos\vartheta^{\prime}_{2}
+ \sin\vartheta_1 \sin\vartheta_2 \cos(\varphi_1 - \varphi_2) \nonumber  \\
&& + \sin\vartheta_1 \sin\vartheta^{\prime}_{2} \cos(\varphi_1 - \varphi^{\prime}_{2})
+ \sin\vartheta^{\prime}_{1} \sin\vartheta_2  \nonumber  \\
&& \times \cos(\varphi^{\prime}_{1} - \varphi_2) - \sin\vartheta^{\prime}_{1}
\sin\vartheta^{\prime}_{2} \cos(\varphi^{\prime}_{1} - \varphi^{\prime}_{2})|
= 2 \sqrt{2}.\end{aligned}$$ Another example which provides the maximum level of violation is $\varphi_1 =\varphi^{\prime}_{1} =\varphi_2 =\varphi^{\prime}_{2} =\varphi_{0}$, $\vartheta_1 =\vartheta_{0} - \pi/4$, $\vartheta^{\prime}_{1}=\vartheta_0 + \pi/4$, $\vartheta_2 =\vartheta_0$, and $\vartheta^{\prime}_{2}=\vartheta_0 -\pi/2$, with $\varphi_0$ and $\vartheta_0$ taking on any arbitrary value. Note that this example includes the previous one when we make $\varphi_0 =0$ and $\vartheta_0 =\pi/4$. In any case, as was shown, to achieve the maximum violation it is necessary that the vectors $\vec{e}_i$ and $\vec{e}\,^{\prime}_{i}$ ($i=1,2$) be perpendicular between themselves. This orthogonality 