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Taking advantage of the strong spin-orbit coupling inherent in three-dimensional topological insulators, we study this phenomenon in Nb/Bi0.8Sb1.2Te3/Nb Josephson weak-link junctions. Under an in-plane magnetic field perpendicular to the current direction, we observe a pronounced Josephson diode effect with efficiencies up to 7%. A crucial component of this behavior is the non-sinusoidal current-phase relationship and an anomalous phase shift, which we attribute to the presence of a ballistic supercurrent component due to the surface states. 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