Fate or Free will: why just one?

Ceci's blog made me rethink of the "Fate or Free will" topic that I chose to avoid in Assignment #1.

"But in effect, [Vonnegut]'s also saying, don't hope, because things are already set in stone." 
This was written in response to the idea that Vonnegut believes in fate over free will. That Vonnegut "thinks everything is predestined". Although I agree with Ceci wholeheartedly on Vonnegut's perceptive of fate and free will, a question came to me: why just one?

Take this for example (which was also taken from one of Ceci's posts); Billy gets on the plane even though he knew it would crash and he also still spoke in public even though he knew he was going to get shot.   
From dictionary.com, free will was defined as "free and independent choice; voluntary decision". Billy chose to get on the plane knowing that it would crash. and he chose to speak in public knowing that he was going to get shot. Those are all his independent choices, something that he decided by himself (for once). To put it simply, he chose to believe in fate. 
 
To me, fate and free will are linked. I believe that it's not one or the other, but both at the same time. It's true that Billy Pilgrim was a character who believed in fate. But that was his choice. Just because he believed that everything was predestined, it doesn't mean that he didn't have any free will (or lack of).  It's true that Billy could have looked at his fate in a more optimistic perceptive like the couple in "Fated To Love You", but wasn't that also his own choice to look at it in a pessimistic point of view? 

In my opinion, it all comes down to this:
If you believed in fate, that was because of your free will. It chose to believe in fate.
If you believed in free will, that was fate. It was destined for you to believe in your own free will.

So if someone asked me whether I believed in fate or free will, I would answer: why just one?

Poo-tee-wee
                                                                 - Yuemin