In coordinate space, consider three planes $E_{1}: x + y + z = 7$, $E_{2}: x - y + z = 3$, $E_{3}: x - y - z = -5$. Let $L_{3}$ be the line of intersection of $E_{1}$ and $E_{2}$; $L_{1}$ be the line of intersection of $E_{2}$ and $E_{3}$; $L_{2}$ be the line of intersection of $E_{3}$ and $E_{1}$. Explain that among $L_{1}, L_{2}, L_{3}$, the acute angle between any two lines is $60^{\circ}$. (Note: Let the acute angle between $L_{1}$ and $L_{2}$ be $\alpha$, the acute angle between $L_{2}$ and $L_{3}$ be $\beta$, and the acute angle between $L_{3}$ and $L_{1}$ be $\gamma$)
In coordinate space, consider three planes $E_{1}: x + y + z = 7$, $E_{2}: x - y + z = 3$, $E_{3}: x - y - z = -5$. Let $L_{3}$ be the line of intersection of $E_{1}$ and $E_{2}$; $L_{1}$ be the line of intersection of $E_{2}$ and $E_{3}$; $L_{2}$ be the line of intersection of $E_{3}$ and $E_{1}$.\\
Explain that among $L_{1}, L_{2}, L_{3}$, the acute angle between any two lines is $60^{\circ}$.\\
(Note: Let the acute angle between $L_{1}$ and $L_{2}$ be $\alpha$, the acute angle between $L_{2}$ and $L_{3}$ be $\beta$, and the acute angle between $L_{3}$ and $L_{1}$ be $\gamma$)