Ugly co-founder breakup

Hi everyone, We are 3 founders with equal shares and equal legal rights in our startup (a Delaware C corp). Recently, we've had some issues with one of our co-founders who has stopped performing and we also discovered he lied about some agreements we made within the founding team at the time of incorporation. Long story short, he wants to leave, and we also want him to leave. However, it's become contentious as the departing co-founder has threatened to screw us up. We incorporated just six months ago, so his shares are unvested (which he is unaware of, as he doesn't really pay attention to legal details). He has demanded half of the investment we've received so far to buy back his shares, even though he is not entitled to it. We know we can call a board meeting to remove him, but we are almost certain he will not sign the share repurchase agreement, even though our company has the contractual right to repurchase all his unvested shares at nominal value. If he refuses to sign, what are our options other than litigation? Any advice would be greatly appreciated. Thanks in advance!