Let the product of \( \omega_1 = (8 + i) \sin \theta + (7 + 4i)\cos \theta \) and \( \omega_2 = (i + 8i)\sin \theta + (4 + 7i)\cos \theta \) be \( \alpha + i\beta \), \( i = \sqrt{-1} \). Let \( p \) and \( q \) be the maximum and the minimum values of \( \alpha + \beta \) respectively. Then \( p + q \) is equal to
