how to display Sin[Subscript[\alpha,i]/2] as $s_{bar{\alpha}_2}$ using e.g., Makeboxes?

I learnt that we can use Makeboxes to display Sin[\alpha_i] as $ s_{\alpha_i}$ as follows:

  (*MakeBoxes[Sin[Subscript[\[Alpha],i_]],StandardForm]:=  MakeBoxes[Subscript[Subscript["s",\[Alpha]],i],StandardForm] 

but can’t find a way to make Sin[Subscript[[Alpha],i]/2] display as $ s_{\bar{\alpha}_2}$ , regardless of in fraction form or in $ a/b$ form. I have been looking for this for quite a long time, but with no luck. I checked the documentation, but can’t understand how Makeboxes works, especially in this context.

Could someone help to produce such a way so that it can take effect on both calculations involving fraction form or $ a/b$ form? It’d be even better if some explanation on how to do it is provided.