Safety and Efficacy Study of Vintafolide and Vintafolide Plus Paclitaxel Compared to Paclitaxel Alone in Participants With Triple Negative Breast Cancer (TNBC) (MK-8109-004)

During treatment, participants receive IV vintafolide 2.5 mg.

During treatment, participants receive IV paclitaxel 80 mg/m\^2.

During screening and prior to screening CT scan, participants receive an IV injection of 0.1 mg etarfolatide radiolabeled with 20 to 25 milliCuries of technetium-99m.

During screening and prior to etarfolatide injection and screening CT scan, participants receive an IV injection of 0.5 mg folic acid.

During treatment, participants receive dexamethasone 20 mg orally 12 to 6 hours prior to paclitaxel; OR promethazine 25 mg or 50 mg IV 30 to 60 minutes prior to paclitaxel; OR cimetidine 300 mg IV or ranitidine 50 mg IV 30 to 60 minutes prior to paclitaxel.