fibonacci numbers - How to evaluate the series $sum_{n=1}^infty frac{1}{F_{4n}}$? Where $F_1=1$, $F_2=1$ and $F_n=F_{n-1}+F_{n-2}$

How would I go about evaluating the following series:

$$\sum_{n=1}^\infty \frac{1}{F_{4n}}$$

Where $F_1=1$, $F_2=1$ and $F_n=F_{n-1}+F_{n-2}$ for $n \ge 3$

Not sure how to go about this except maybe by using the close form for the nth fibonacci number, but that seems like way too much arithmetic. Any ideas?