$\text{ The angle between any two diagonals of a cube is }$

$\text{ Direction ratios of }OP\text{ are }<a,a,a>\text{ or }<1,1,1>$

$\text{ and those of }AL\text{ are }<-a,a,a>\text{ or }<-1,1,1>$

$\therefore \cos \theta =\frac{-1+1+1}{\sqrt{3}\cdot \sqrt{3}}=\frac{1}{3}$