The plane passing through the line L: l x-y+3(1-l) z=1, x+2 y-z=2 and perpendicular to the plane 3 x+2 y+z=6 is 3 x-8 y+7 z=4. If θ is the acute…

The plane passing through the line $\displaystyle L: l x-y+3(1-l) z=1, x+2 y-z=2$ and perpendicular to the plane $\displaystyle 3 x+2 y+z=6$ is $\displaystyle 3 x-8 y+7 z=4$. If $\displaystyle \theta$ is the acute angle between the line $\displaystyle L$ and the $\displaystyle y$-axis, then $\displaystyle 415 \cos ^2 \theta$ is equal to \_\_\_\_.