Geometrical Matrix

Geometry Level 3

\[\begin{bmatrix}{\cos\left(\frac{2\pi}7\right)} & {-\sin\left(\frac{2\pi}7\right)} \\ {\sin\left(\frac{2\pi}7\right)} & {\cos\left(\frac{2\pi}7\right)}\end{bmatrix} ^k = \begin{bmatrix}{1} &{0} \\ {0} & {1}\end{bmatrix} \]

Find the least positive integral value of \(k\) which satisfy the matrix equation above.