homework and exercises - Shell model of an odd-odd nucleus: $^6$Li

Lithium-6 isotope has an approximate magnetic momentum of $0.88\ \mu_N$ in its fundamental nuclear state. I'm trying to find its angular momentum and parity.

I found in a standard table: $I=1^+$ and while I get the parity part, I don't understand the rest. What I have done is filling the shells separately for protons and neutrons and finding that both have their outer particle in the $1 P_{3/2}$ state. Sum of these gives possible total angular momenta to be either $0$, $1$, $2$ or $3$.

So my question is: how do you choose between these to find the real value $I=1$?