Fourier Fun

$x= \lim_{p\to\infty} \int_0^\pi \int_0^z \dfrac{ \sin(py/2) }{\sin(y/2)} \cos\left( \dfrac{(p+1)y}2 \right) \, dy \; dz$

$p$ is an integer. Find $\lfloor 69x \rfloor$ .