I thoroughly agree that the central idea of the Bhagavad Gita is to do your job without unnecessary worry or anxiety about the outcome. I've seen similar ideas in Epictetus's Enchiridion (put yourself to things in your control and forget about things beyond your power) and more recently in the notion of "separation of tasks" central to Alfred Adler's works. Irrespective of the source, the idea of focussing on my job without worrying about the outcome has been immensely helpful to me in moments of great anxiety and uncertainty.