Use the fact that $\operatorname{cos}(2θ) = 2\operatorname{cos}^2 θ − 1$ to evaluate the following integrals.

1. $\int _ { 0 } ^ { 2 \pi } \operatorname { cos } ^ { 2 } \theta d \theta$

   Step (a):

   $=\frac{1}{2}\int_0^{2\pi}\Big(\cos(2\theta)+1\Big)d\theta$

2. $\int _ { 0 } ^ { 2 \pi } 4 \operatorname { sin } ^ { 2 } \theta d \theta$

   Hint (b):

   $2\sin^2(\theta)=1-\cos(2\theta)$