Let a line \(L\) be perpendicular to both the line \({L}_{1}:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}\) and \({L}_{2}:\…

Let a line \(L\) be perpendicular to both the line \({L}_{1}:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}\) and \({L}_{2}:\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}\). If \(\theta\) is the acute angle between the lines \(L\) and \({L}_{3}:\frac{x-\frac{8}{7}}{2}=\frac{y-\frac{4}{7}}{1}=\frac{z}{2}\), then \(\tan \theta\) is equal to:

[JEE Main 2026, 6 Apr (Shift 1)]