Let \( \vec{p} = 2\hat{i} + \hat{j} + 3\hat{k} \) and \( \vec{q} = \hat{i} - \hat{j} + \hat{k} \). If for some real number \( \alpha, \beta \) and \( \gamma \), we have
\( 15\hat{i} + 10\hat{j} + 6\hat{k} = \alpha(2\vec{p} + \vec{q}) + \beta(\vec{p} - 2\vec{q}) + \gamma(\vec{p} \times \vec{q}) \), then the value of \( \gamma \) is ________________.
