Straight Lines And Pair Of Straight Lines

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 \(\mathrm{ABCD}\). If \(A B=\sqrt{10}\) and the points \(\mathrm{A}\) and \(\mathrm{C}\) lie on the line \(3 y=2 x+1\), then \(2(\alpha+\beta+\gamma+\delta)\) is equal to