Let a vector a =√ 2 i - j +λ k, λ>0, make an obtuse angle with the vector b =-λ^2 i +4 √ 2 j +4 √ 2 k and an angle θ, (π)/6<θ<(π)/2, with the…

Let a vector $\displaystyle \overrightarrow{\mathrm{a}}=\sqrt{2} \hat{i}-\hat{j}+\lambda \hat{k}, \lambda>0$, make an obtuse angle with the vector $\displaystyle \overrightarrow{\mathrm{b}}=-\lambda^2 \hat{i}+4 \sqrt{2} \hat{j}+4 \sqrt{2} \hat{k}$ and an angle $\displaystyle \theta, \frac{\pi}{6}<\theta<\frac{\pi}{2}$, with the positive $\displaystyle z$-axis. If the set of all possible values of $\displaystyle \lambda$ is $\displaystyle (\alpha, \beta)-\{\gamma\}$, then $\displaystyle \alpha+\beta+\gamma$ is equal to $\displaystyle \_\_\_\_$.