For \( \lambda > 0 \), let \( \theta \) be the angle between the vectors \( \vec{a} = \hat{i} + \lambda \hat{j} - 3\hat{k} \) and \( \vec{b} = 3\hat{i} - \hat{j} + 2\hat{k} \). If the vectors \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) are mutually perpendicular, then the value of \( (14\cos\theta)^2 \) is equal to:
