The cancellation of projective modules of rank 2 with a trivial determinant

We study the cancellation property of projective modules rank $2$ with a trivial determinant over Noetherian rings dimension $\leq 4$. If $R$ is smooth affine algebra $4$ an algebraically closed field $k$ such that $6 \in k^{\times}$, then we prove stably free $R$-modules are if and only Hermitian $K$-theory group $\tilde{V}_{SL} (R)$ trivial.