Can one of the doctrines of Hinduism lead to fatalistic thinking?

I haven't read all the Bhagavad Gita, but I've read some of it and I wanted to ask about the idea that we're supposed to just do whatever was given to us as our "duty" and leave the results to God (or the Universe or whatever you want to call it). I don't know if that doctrine has an official name to it. But I know there's a principle in psychology called "locus of control", that people are mentally healthy to the extent that they believe they have control over what happens to them. If we can't expect to have control over the results of our actions, or at least predict with a degree of certainty, won't that lead to fatalistic thinking?