## Tricky infinite sum to enter into computation program

Hi,

Can anyone think of a way to input the following infinite sum into Maxima for computation?

$\sum_{n=0}^{\infty }2^{n-1}c_n^2$

(The tricky part...)

where $c_0=\sin\theta$

and $\sin\theta_{n+1}=\frac{1-\cos\theta_n}{1+\cos\theta_n}$