# Bounding Fejer kernel

My Ferjer kernel is defined to be $F_N(t):= \frac{1}{N+1}(\frac{sin(N+1)\pi t}{sin \pi t})^2$, I want to show that $F_N(t) \leq \frac{c}{N+1}min\{N+1, \frac{1}{x^2}\}$ on $[\frac{1}{-2}, \frac{1}{2}]$.

Thoughts: I need some kind of bound on $sin(N+1)\pi t$, but I do not see how to derive a useful bound.