To simplify the expression, we first need to square the complex number ( \left( \cos \frac{\pi}{3} + i \sin \frac{\pi}{3} \right) ):

( \left( \cos \frac{\pi}{3} + i \sin \frac{\pi}{3} \right)^2 )

Using De Moivre's Theorem, we have:

( \cos \frac{2\pi}{3} + i \sin \frac{2\pi}{3} )

Thus,

( \left( \cos \frac{2\pi}{3} + i \sin \frac{2\pi}{3} \right) )