Serial Imaging of the Novel Radiotracer [^18F] FLuorthanatrace ([^18F] FTT) by PET/CTF

PRIMARY OBJECTIVES: \- Evaluate fluorine F 18 fluorthanatrace (\[18F\]Fluorthanatrace) positron emission tomography/computed tomography (PET/CT) as an imaging biomarker of poly \[ADP-ribose\] polymerase (PARP)-1 activity in 3 cohorts of cancer patients: 1) ovarian, fallopian tube, primary peritoneal 2) breast cancer, and 3) non-ovarian, non-breast solid tumor. SECONDARY OBJECTIVES: * Evaluate the safety of \[18F\]Fluorthanatrace. * Correlate \[18F\]Fluorthanatrace uptake measures with BRCA mutation status. * Correlate \[18F\]Fluorthanatrace uptake measures with poly \[ADP-ribose\] polymerase (PARP-1) activity in tumor tissue samples in patients who undergo biopsies. * Evaluate change in \[18F\]Fluorthanatrace uptake measures after therapy initiation with repeat imaging before and after treatment initiation. * To confirm the variability of imaging findings from repeated \[18F\]FTT PET/CT over 1 week before treatment initiation * Determine the change in \[18F\]FluorThanatrace uptake before treatment initiation and at time of clinical progression * Correlate \[18F\]FluorThanatrace uptake at time of clinical progression measures with genetic reversion mutation status OUTLINE: Patients receive fluorodeoxyglucose (FDG) intravenously (IV) and undergo FDG PET/CT scan over 20-30 minutes if they have not already had one per standard of care. At least 20-24 hours later, patients receive fluorine F 18 fluorthanatrace IV and undergo fluorine F 18 fluorthanatrace (\[18F\]FTT) PET/CT over 1 hour. After completion of study treatment, patients are followed up at 24 hours.