Thank you for such a serious question. I think all three are reconciled by the ethic of mutual respect (of a basic kind: taking one another into account as we live our separate lives together in this world). At a minimum, such respect requires that we refrain from killing, harming, coercing, stealing, or manipulating (lying, cheating, etc.) to get what we want--whether for ourselves, for any other(s), in business, or in politics.

A requirement of respect of that kind follows from a belief in equality. Respecting one another that way in our direct, personal interactions with one another and applying that ethic to the political process and the economy would provide the maximum liberty that co-existing people can share. (I maintain that mutual respect of that kind already forms the ethical foundation of ‘democracy’ and have developed a way to apply it to the economy as a system.)

I've frankly never considered "Fraternity" per se, but I have thought about the relationship of that ethic to the teachings of Jesus. I believe mutual respect of that kind is the 'minimum condition' of Jesus's "righteousness" in our relations with one another.

If curious, all but that last part is explained more fully in "Equality Is All We Need" (here in Medium).