Background: Several approaches are currently trying to understand the generation of angular momentum in the fission fragments. The microscopic TDDFT and statistical FREYA lead to different predictions concerning the opening angle distribution formed between the two spins in particular at 0 and 180 degrees.

Purpose: This Letter aims to investigate how the geometry and the quantum nature of spins impact the distribution of opening angles to understand what leads to different model predictions.

Method: Various assumptions of $K$ distribution ($K=0$, isotropic, isotropic with total $K=0$, and from TDFFT) are investigated in a quantum approach. These distributions are then compared to the classical limit using the Clebsch-Gordan coefficients in the limit of $\hslash$ approaches zero.

Results: It is shown that in all the schematic scenario the quantal distribution of opening angle lead to the expected behavior in the classical limit. The model shows that the quantal nature of the spins prevents the population of opening angles close to 0 and 180 degrees. The difference in opening angle in the two-dimensional and isotropic three-dimensional distribution is discussed and it is shown that the realistic TDFFT opening angle distribution presents an intermediate behavior between the two cases.

Conclusions: The last comparison reveals two key differences between the two model's predictions: the quantal spins' nature in TDDFT and the assumption of zero $K$ values in FREYA.

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