So, Mathematica can't solveevaluate it. Any workaround?
\begin{equation*} \int_0^\pi \frac{1}{\sin\left(\frac{\theta}{2}\right)^\beta + 1} \mathrm{d}\theta \end{equation*}$$\int_0^\pi \frac{\mathrm{d}\theta}{\sin\left(\frac{\theta}{2}\right)^\beta + 1}$$
The code is:
Integrate[1/(Sin[θ/2]^β + 1), {θ, 0, π}]