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Triple-negative breast cancer (TNBC) is an aggressive malignancy that requires effective targeted drug therapy. In this study, we employed in silico methods to evaluate the efficacy of seven approved drugs against human ck2 alpha kinase, a significant modulator of TNBC metastasis and invasiveness. Molecular docking revealed that the co-crystallized reference inhibitor 108600 achieved a docking score of (-7.390 kcal/mol). Notably, among the seven approved drugs tested, sunitinib, bazedoxifene, and etravirine exhibited superior docking scores compared to the reference inhibitor. Specifically, their respective docking scores were -10.401, -7.937, and -7.743 kcal/mol. Further analysis using MM/GBSA demonstrated that these three top-ranked drugs possessed better binding energies than the reference ligand. Subsequent molecular dynamics simulations identified etravirine, an FDA-approved antiviral drug, as the only repurposed drug that demonstrated a stable and reliable binding mode with the human ck2 alpha protein, based on various analysis measures including RMSD, RMSF, and radius of gyration. Principal component analysis indicated that etravirine exhibited comparable stability of motion as a complex with human ck2 alpha protein, similar to the co-crystallized inhibitor. Additionally, Density functional theory (DFT) calculations were performed on a complex of etravirine and a representative gold atom positioned at different sites relative to the heteroatoms of etravirine. The results of the DFT calculations revealed low-energy complexes that could potentially serve as guides for experimental trials involving gold nanocarriers of etravirine, enhancing its delivery to malignant cells and introducing a new drug delivery route. Based on the results obtained in this research study, etravirine shows promise as a potential antitumor agent targeting TNBC, warranting further investigation through experimental and clinical assessments.