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Spontaneous rotational-symmetry breaking in the superconducting state of doped Bi₂Se₃ has attracted significant attention as an indicator for topological superconductivity. High-resolution calorimetry of single-crystal Sr_0.1Bi₂Se₃ provides unequivocal evidence of a twofold rotational symmetry in the superconducting gap by a bulk thermodynamic probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's low carrier concentration proving bulk superconductivity. The large basal-plane anisotropy of H_c2 is attributed to a nematic phase of a two-component topological gap structure η = (η₁, η₂) and caused by a symmetry-breaking energy term δ(|η₁|² - (|η₂|²) T_c. A quantitative analysis of our data excludes more conventional sources of this two-fold anisotropy and provides the first estimate for the symmetry-breaking strength δ ~ 0.1.