Filter impulse response calculation

Hi,

This is a basic Introduction to DSP question:
I have a discrete time filter whose impulse repsone DTFT is given in the attached file. I need to find the inverse DTFT h_notch[n].

The clue says to first express Hnotch through Hlp which is
also given in the attached file.

First, I'm having trouble expressing Hnotch through Hlp.
And second, why the two points of discontinuity in Hnotch even
effect the IDTFT integral?

thanks for the help.