Outline a method of synthesizing \(\alpha\) -phenylethyl tert-buty1 ether from styrene and tert-butyl alcohol. Any inorganic reagents may be employed.

To synthesize α-phenylethyl tert-butyl ether from styrene and tert-butyl alcohol, follow these steps: 1. Deprotonate tert-butyl alcohol with sodium hydride (NaH) to form the tert-butoxide ion: \[ tert\text{-}butyl\,alcohol + NaH \rightarrow tert\text{-}butoxide\,Na+ + H_2 \] 2. React styrene with N-bromosuccinimide (NBS) for benzylic bromination to produce α-phenylethyl bromide: \[ styrene + NBS \rightarrow \alpha\text{-}phenylethyl\,bromide \] 3. Perform Williamson Ether Synthesis by reacting the tert-butoxide ion with α-phenylethyl bromide, resulting in the desired ether product and a by-product: \[ tert\text{-}butoxide\,Na+ + \alpha\text{-}phenylethyl\,bromide \rightarrow \alpha\text{-}phenylethyl\,tert\text{-}butyl\,ether + NaBr \]