$\nabla\times(\nabla\times(\nabla\times A))$ using Levi-Civita tensor

Question

Knowing the fact that $\nabla\times(\nabla\times A)=\nabla(\nabla\cdot A)-(\nabla\cdot\nabla)A$, can anyone help me in calculating $\nabla\times(\nabla\times(\nabla\times A))$ using Levi-Civita tensor?