Rotating Indices Property of Vector Triple Product

Theorem
Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be vectors in a Euclidean $3$-space.

Then:
 * $\mathbf a \times \paren {\mathbf b \times \mathbf c} + \mathbf b \times \paren {\mathbf c \times \mathbf a} + \mathbf c \times \paren {\mathbf a \times \mathbf b} = 0$

where $\mathbf a \times \paren {\mathbf b \times \mathbf c}$ denotes the vector triple product operator.