Solve θ^{i}=-1/2varepsilon^ijkomega^jktext{and}v^i=omega^0i

$$\theta ^ { i } = - \frac { 1 } { 2 } \varepsilon ^ { i j k } \omega ^ { j k } \text { and } v ^ { i } = \omega ^ { 0 i }$$

Solve for θ, ε, j, k, ω, v

$$\theta =2^{i}\left(|\epsilon ^{ijk}||\omega ^{jk}|\right)^{-i}e^{arg(-\epsilon ^{ijk}\omega ^{jk})-2\pi n_{1}}$$

$$n_{1}\in \mathrm{Z}$$

$$\epsilon \in \mathrm{C}$$

$$j\in \mathrm{C}$$

$$k\in \mathrm{C}$$

$$\omega \neq 0$$

$$v=\frac{1}{e^{2\pi n_{2}}}$$

$$n_{2}\in \mathrm{Z}$$