Answer
$\theta=\arccos \left(\frac{2}{\sqrt{6}}\right)$
Work Step by Step
The diagonal of a cube can be represented by the vector u=(1,1,1) and one
of its sides can be represented by v=(1,1,0). Then, the angle between u and v is given by
$\theta=\arccos \left(\frac{u \cdot v}{\|u\|\|v\|}\right)=\arccos \left(\frac{2}{\sqrt{6}}\right)$
