Oops! I meant to write e^(iτ) - 1 = 0. I was going back and forth between the various formulations of the identities:

  e^(iπ) + 1 = 0,
  e^(iτ) - 1 = 0,
  e^(iπ) = -1,
  e^(iτ) = 1.

The one involving pi looks more elegant when written in the first manner. The one involving tau looks more elegant when written in the fourth manner. I screwed up this one while going back and forth between these options. I have fixed it now. Thanks for noticing and commenting!