The total angular momentum of a bound state of quarks, such as a meson say, can be done by studying the spin and orbital angular momentum of the 2 valence quarks.
What about the sea quarks why they do not contribute? or do they?
I will tackle the experimental part leaving the theoretical for the adepts of QCD on the lattice, as the link dmckee provided in the comments clarifies.
This is a picture of a gluon and a quark antiquark pair, in OPAL.
The corresponding Feynman diagram is
We see here that out of the blue, the energy inputed by the incoming electron positron pair becomes an offshell photon ( spin 1) and a quark antiquark pair (spin 1/2 each) , with a gluon (spin 1) emitted from one of them . The total angular momentum must add up to the spin of the photon that gave birth to them.
Note that by quantum numbers the three end products could be within a bound meson, if the energy were lower. The algebra is the same.
We know just the total spin of the meson, because we have measured it, not how the quarks and gluons inside add up to give the measured value. For example the quarks could add up to zero spin and the spin observed be the spin of the gluon, in the picture above. In a pion which has zero spin all spins must add up to zero. The total spin does not tell us any details about the internal spin form factors unless we do specialized experiments as in the link above.
Do you have a link for this? We only have measurements for the spin of the bound states of quarks. The quark model does not depend on the quark spins except as a limit in conservation of angular momentum .
For example in the meson octet:
The spin does not enter in the symmetry pattern classification, it characterizes the whole representation.
Logic says that they must since angular momentum is not like charge and strangeness, simply additive.
I don't know if I'm right and it's not directly my topic, but naively guessing I think that sea quarks emerge from fluctuations in the vacuum, for example as a pair of a quark and its antiquark. And as such, because of conservation of angular momentum, each of these pairs then should have zero total angular momentum.