Sequences And Series

Let \(0 < z < y < x\) be three real numbers such that \(\frac{1}{x}, \frac{1}{y}, \frac{1}{z}\) are in an arithmetic progression and \(x, \sqrt{2} y, z\) are in a geometric progression. If \(x y+y z+z x=\frac{3}{\sqrt{2}} x y z\) , then \(3(x+y+z)^{2}\) is equal to ____________.