Let the product of $w_1 = (8 + i)\sin\theta + (7 + 4i)\cos\theta$ and $w_2 = \cos\theta + (4 + 7i)\sin\theta$ be $a + i\beta$, $i = \sqrt{-1}$. Let $p$ and $q$ be the maximum and the minimum values of $a + \beta$ respectively. Then $p - q$ equals: