Let \( \alpha, \beta, \gamma, \delta \in \mathbb{Z} \) and let \( A(\alpha,\beta) \), \( B(1,0) \), \( C(\gamma,\delta) \) and \( D(1,2) \) be the vertices of a parallelogram \( ABCD \). If \( AB=\sqrt{10} \) and the points \( A \) and \( C \) lie on the line \( 3y=2x+1 \), then \( 2(\alpha+\beta+\gamma+\delta) \) is equal to:
