겠

I will; that must be

Two closely related jobs. It announces the speaker's own intention — "I'll start now", "I'm looking forward to it", "I need to study this and tell you" — and it reads a situation as very likely, giving "that must have been" or "that could work". It also sits inside the standard way of saying "I hope", which is what several examples are doing when they wish the audience enjoyed something. It goes inside the word, right before the final ending, so it is easy to miss.