Why stalking Betty in her flat? (SPOILER)

One thing I don't get in "Opera" is why the killer had to enter in Betty's apartment by killing Mira. What was his pourpose? He had already enjoyed tiding and harassing her just hours before while murdering the costumist at the theatre so I don't understand why he had to burst into the house at all costs.

Besides this I find very tender the moment Betty bumps into the ispector on her way home and he grabs her wrists wounded by the rope. He demands some explanations and she opens to him very sweetly explaining the killer's "modus operandi" not knowing he his the man and asking for his protection.

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