Let \(0<z<y<x\) be three real numbers such that \(\frac{1}{x}, \frac{1}{y}, \frac{1}{z}\) are in an arithmetic …

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 ______ .

[JEE Main 2023, 8 Apr (Shift 2)]