Graphs of the Other Trigonometric Functions · Medium problem

By how much is the graph of $y = -2\cot\left(\dfrac{1}{2}x - \dfrac{\pi}{6}\right) + 2$ shifted horizontally compared with $y = -2\cot\left(\dfrac{1}{2}x\right) + 2$? Give the signed shift as an exact multiple of $\pi$ (positive means to the right).