Ex5 19

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 5.19}$

Let $R$ be an irrational rotation about some axis of a sphere. Show that for any other rotation $R'$ about the same axis and for any desired level of approximation $2^{-d}$ there is some power of $R$ that approximates $R'$ to the desired level of accuracy.