<image>As shown in the figure, in right triangle \( \triangle ABC \), \( \angle ACB = 90^\circ \), \( \angle CAB = 30^\circ \), and \( BC = 2 \). Points \( O \) and \( H \) are the midpoints of sides \( AB \) and \( AC \) respectively. Rotate \( \triangle ABC \) around point \( B \) clockwise by \( 120^\circ \) to the position of \( \triangle A_{1}BC_{1} \). Then, the area of the region swept by segment \( OH \) during the entire rotation (i.e., the shaded area) is _________________. 