Brian Armstrong is being patted down with a makeup sponge as a big green screen looms behind him. “Coinbase is a company with an ambitious vision: to create more economic freedom,” he reads off a teleprompter, but flubs the final part of the line. “We’ll try that one again.” The stoic, bald Armstrong, clad in a favorite black jacket, is standing on an empty stage, reciting lines about Coinbase, the company he founded, for a promotional video for investors. A self-described introvert, Armstrong is notoriously averse to media appearances, except in the right context—including taping the 88-minute-long documentary COIN, which the company commissioned. The film, released in early October, documents…