A 10 inches long pencil $A B$ with mid point $C$ and a small eraser $P$ are placed on the horizontal top of a table such that $\mathrm{PC}=\sqrt{5}$ inches and $\angle \mathrm{PCB}=\tan ^{-1}(2)$. 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 :