Techniques of Integration · Hard problem

A rotor's angular speed is $\omega(\theta)=5+3\cos\theta$ rad/s, where $\theta$ is the rotor's own angle. The time to turn from $\theta=0$ to $\theta=\pi$ is $t=\displaystyle\int_0^\pi\dfrac{d\theta}{5+3\cos\theta}$. Find $t$ (in seconds).