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Sincethe Inverse Fourier transforms of phase factors giveand

From $z=\tan w=-i(e^{2iw}-1)/(e^{2iw}+1)$ one obtainsFor $z=(2\sqrt{3}-3i)/7$ the quotient is $1+i\sqrt{3}=2e^{i\pi /3}$. Its principal logarithm is $\log 2+i\pi /3$, so the principal value is

Using Euler's formula and the Inverse Fourier transforms of phase factors,andThese are distributional identities, with $\delta$ the Dirac delta function.