The value of $\sum\limits_{n=1}^{\infty}\large\frac{\tan\bigg(\Large\frac{\theta}{2^n}\bigg)}{2^{n-1}\cos\bigg(\Large\frac{\theta}{2^{n-1}}\bigg)}$ is equal to

Question

$\begin{array}{1 1}(a)\;\large\frac{2}{\sin 2\theta}-\frac{1}{\theta}&(b)\;\large\frac{2}{\sin 2\theta}+\frac{1}{\theta}\\(c)\;\large\frac{1}{\sin 2\theta}-\frac{1}{\theta}&(d)\;\large\frac{2}{\sin\theta}-\frac{1}{\theta}\end{array}$