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