Heaven's Lost Property: Forte

Sakurai Tomoki has settled into his life with the two angeloids, Ikaros and Nymph, and is enjoying himself immensely. However, he keeps having weird dreams and asks all of his friends to help him investigate the cause. Nymph conjures up a device that enables people, but not angeloids, to enter other people's dreams. The device malfunctions at first but eventually they get to what was supposed to...