a) State or imply $dx = 2\cos \theta {\text{ }}d\theta $, or $\frac{{dx}}{{d\theta }} = 2\cos \theta $, or equivalent

Substitute for $x$ and $dx$ throughout the integral

Obtain the given answer correctly, having changed limits and shown sufficient working

b) Replace integrand by $2 - 2\cos 2\theta $, or equivalent

Obtain integral $2\theta  - \sin 2\theta $, or equivalent

Substitute limits correctly in an integral of the form $\alpha \theta  \pm b\,\sin 2\theta $, where $\alpha b{\text{ }}\rho {\text{ }}0$

Obtain answer $\frac{1}{3}\pi  - \frac{{\sqrt 3 }}{2}$ or exact equivalent

[The f.t. is on integrands of the form $\alpha  + c\,\,\cos \,2\theta $, where $\alpha \theta  \pm b\,\sin 2\theta $, where $\alpha b{\text{ }}\rho {\text{ }}0$.]