$\int \limits_0^{\pi} \large\frac{\theta \sin \theta}{1+\cos ^2 \theta} $$ d \theta$ is equal to :

Question

\[\begin {array} {1 1} (a)\;\frac{\pi^2}{2} & \quad (b)\;\frac{\pi^3}{3} \\ (c)\;\pi^2 & \quad (d)\;\frac{\pi^2}{4} \end {array}\]