A \( 10 \) inches long pencil \( AB \) with mid point \( C \) and a small eraser \( P \) are placed on the horizontal top of a table such that \( PC = \sqrt{5} \) inches and \( \angle PCB = \tan^{-1}(2) \). The acute angle through which the pencil must be rotated about \( C \) so that the perpendicular distance between eraser and pencil becomes exactly \( 1 \) inch is:
