Taking into consideration the functions
$$\sum_{t=0}^{n} \sin{(\theta + t \phi)}=\frac{\sin({\frac{(n+1)\phi}2})\sin{(\theta+\frac{n \phi}2)}}{\sin{(\frac{\phi}2)}}$$
and
$$\sum_{t=0}^{n}\cos{(\theta+t\phi)}=\frac{\sin({\frac{(n+1)\phi}2})\cos{(\theta+\frac{n \phi}2)}}{\sin{(\frac{\phi}2)}}$$
Find, for all $\theta$, the values of
$$\sum_{t=0}^{n}\cos^{2}{(2t\theta)} \quad \textrm{and} \quad\sum_{t=0}^{n}\sin^{2}{(2t\theta)}$$