Let $$\alpha, \beta$$ be the roots of the equation $$x^2 - 4\lambda x + 5 = 0$$ and $$\alpha, \gamma$$ be the roots of the equation $$x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0$$. If $$\beta + \gamma = 3\sqrt{2}$$, then $$(\alpha + 2\beta + \gamma)^2$$ is equal to ______