integrating sin(nx)/sin(x)

integrating sin(nx)/sin(x)

I have an definite integral of the form:
\int \frac{\sin(n\theta(x)))}{\sin(\theta(x))} dx.
Theta is a function of x (and actually a complicated one).
Is it possible to integrate it --- analytically and/or numerically? The
Dirichlet kernel for fourier series makes me feel very optimistic about
this one because they appear so similar. But I am not able to go too far
with it.
What if the integral was a definite integral? like -- from x = 0 to x = pi/2.