In quantum mechanics, the angle between two angular momentum vectors is not really defined. That is because at least two components of a nonzero angular momentum vector are uncertain. However, the inner product of angular momentum vectors can be well defined. In some sense, that gives an angle between the two vectors.
An important case is the inner product between the spins of two
particles. It is related to the square net combined spin of the
particles as
Now an elementary particle has a definite square spin angular momentum
As an important example, consider two fermions with spin
. These fermions may be in a singlet state
with combined spin 0. Or they may be in a
triplet state with combined spin 1. If that is
plugged into the formulae above, the inner product between the spins
is found to be
Based on that, you could argue that in the singlet state the angle between the spin vectors is 180. In the triplet state the angle is not zero, but about 70.