If the vectors \( \vec{a} = \lambda \hat{i} + \mu \hat{j} + 4\hat{k} \), \( \vec{b} = -2\hat{i} + 4\hat{j} - 2\hat{k} \) and \( \vec{c} = 2\hat{i} + 3\hat{j} + \hat{k} \) are coplanar and the projection of \( \vec{a} \) on the vector \( \vec{b} \) is \( \sqrt{54} \) units, then the sum of all possible values of \( \lambda + \mu \) is equal to:
