desmonterarse

A rare, specialized bullfighting term: to take off one's montera, the traditional black hat worn by a matador, usually as a gesture of tribute or respect — brindando la faena tras desmontararse ('offering the performance after removing the hat'). You'll only encounter it in writing about tauromaquia.

• El torero se desmonteró en honor al maestro fallecido. — The bullfighter removed his hat in honor of the deceased master.
• Se desmonteró antes de brindar la faena al público. — He took off his montera before dedicating the performance to the crowd.
• Los aficionados esperaban el momento en que se desmonterara. — The fans awaited the moment he would remove his montera.

This is bullfighting-specific vocabulary a learner will only meet in tauromaquia writing — there's no everyday confusion to flag, since general Spanish has no competing verb for this precise gesture.