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Scrape off as much of the ceiling star adhesive as possible with a metal scraper. Insert the edge of the scraper under the adhesive and carefully slide the scraper, in a side-to-side motion, until you've wedged the scraper underneath the adhesive. Lift the scraper and peel off as much adhesive as possible.
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Combine 1 pint warm water with 1 tsp. dish washing detergent and 1 tbsp. white vinegar. Soak a clean cloth with the warm detergent and vinegar solution and wring out excess moisture.
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Hold the cloth over the remaining adhesive for 30 seconds. Scrub the the cloth back and forth over the adhesive, which should cause it to ball up. Continue to scrub the adhesive backing to remove as much as you can.
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Spray the last traces of adhesive backing with lubricating spray used for greasing hinges or squeaky doors. Rub the lubricating spray into the adhesive with a clean, dry cloth until it's completely removed.
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Wash the ceiling surface with the dish soap and vinegar solution to remove greasy residue from the lubricating spray. Rinse the ceiling by wiping it off with a damp cloth.