These gorgeous birds are called rufous treepie, their Bengali name is hanrichancha that roughly means the “sound of scraping metal vessels”. They do have a raucous voice. There are three of them in this area, at least, and when they are not chasing each other they sing very sweetly!
They are neither shy nor fearless, you can see, s/he was almost ignoring me. In few of the shots I have seen her checking me/my camera out 🙂