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