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 \( x^{2}-\left(3\sqrt{2}+2\sqrt{3}\right)x+7+3\lambda\sqrt{3}=0 \), \( \lambda>0 \). If \( \beta+\gamma=3\sqrt{2} \), then \( (\alpha+2\beta+\gamma)^{2} \) is equal to _______.
