The period of the discrete-time signal \(x[n]\) described by the equation below is \(N =\) ..................... (Round off to the nearest integer).
\[
x[n] = 1 + 3\sin\!\left(\frac{15\pi}{8}n + \frac{3\pi}{4}\right) - 5\sin\!\left(\frac{\pi}{3}n - \frac{\pi}{4}\right)
\]