Final answer:
To calculate the average value of the angular momentum around a z'-axis that makes an angle θ' with the z-axis, we need more information about the eigenstate ψ.
Step-by-step explanation:
The average value of the angular momentum around a z'-axis that makes an angle θ' with the z-axis can be calculated using the eigenstate ψ of J^2 and J_z. The average value of the angular momentum can be computed as:
L'_z = ⟨ψ|J'_z|ψ⟩
where J'_z is the z-component of the angular momentum along the z'-axis.
To calculate this average value, we need to know the specific form of the eigenstate ψ.
Please provide more information about the eigenstate to proceed with the calculation.