Question 75
What is the largest real number $\theta$ less than $\pi$ (i.e. $\theta\lt \pi$ ) such that
$$
\prod_{k=0}^{10} \cos \left(2^{k} \theta\right) \neq 0
$$
and
$$
\prod_{k=0}^{10}\left(1+\frac{1}{\cos \left(2^{k} \theta\right)}\right)=1 ?
$$
$$
\prod_{k=0}^{10} \cos \left(2^{k} \theta\right) \neq 0
$$
and
$$
\prod_{k=0}^{10}\left(1+\frac{1}{\cos \left(2^{k} \theta\right)}\right)=1 ?
$$