How to make my equation fancier?

[PhyAmateur]

Hello!
I hope I am posting this in the right thread!
As I was solving a problem in general relativity, my final answer needs to get a little fancier. So my final answer was as follows: $$ (\bar{U}{U})^3 (\epsilon_{ijk} \frac{d\omega^i}{dx^k} \theta^k) \wedge (\epsilon_{ijk} \frac{d\omega^i}{dx^k} \theta^k) $$ But if my theta's are equal to one another they will eat themselves out. This mean for example $$(\theta^1 \wedge \theta^1 = 0)$$ So I don't know if using some neat maths trick I can write out my final answer without the need to put a note of what I just wrote. How to make the equation speak for itself?

Thank you!

 

[Ben Niehoff]

You need to rename some dummy indices in the second factor so that each index is repeated only twice. Then use

$$\varepsilon_{abc} \varepsilon_{ade} = \delta^{bc}_{de} = \delta^b_d \delta^c_e - \delta^c_d \delta^b_e$$