Rather than merely resolving to overcome the fear, I'd make myself imagine what's supposed to be so bad about the thing I'm afraid of (not being top-.001% gifted? being destroyed by an expert? that both occur in view of others?), and reassure myself that the feared outcome is not actually so terrible.
However, making a public resolution is also a good approach.
The word "platitude" springs to mind, as well as the phrase "it's easier said than done." Everyone knows the basic processes of cognitive behavioral therapy; it's applying them when you're actually feeling anxiety that's hard.
I agree that it's not easily done. If thinking about the fear abstractly doesn't work (it probably won't), actually allow yourself to imagine/feel the negatives you believe as concretely as possible. I don't see how you can approach knowing what's really going on in your own mind if you're unwilling to observe without trying to suppress and control.
I can accept that reasoning away the specific concerns/self-beliefs isn't always possible. Some things really are hard and require practice, even after obviously buggy internal thoughts (usually exaggeration of the negative consequences you risk by trying) are refuted.
However, making a public resolution is also a good approach.