If $n \equiv 0,1~mod~4$, we prove a sum formula $V_{ \theta_{ 0}} (a_{ 0},a_{ R}^{ n}) = n \cdot V_{ \theta_{ 0}} (a_{ 0},a_{ R})$ for the generalized Vaserstein symbol whenever $R$ is a smooth affine algebra over a perfect field $k$ with $char(k) \neq 2$ such that $-1 \in { k^{ \times}}^{ 2}$. This enables us to generalize a result of Fasel-Rao-Swan on transformations of unimodular rows via elementary matrices over normal affine algebras of dimension $d \geq 4$ over algebraically closed fields of characteristic $\neq 2$. As a consequence, we prove that any projective module of rank $3$ with trivial Chern classes over a smooth affine algebra of dimension $4$ over an algebraically closed field $k$ with $char(k) \neq 2,3$ is cancellative.
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