This pilot clinical trial studies docetaxel and carboplatin in treating patients with castration resistant prostate cancer that has spread from the primary site (place where it started) to other places in the body (metastatic) and contains inactivated genes in the BRCA 1/2 pathway. Drugs used in chemotherapy, such as docetaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading.