Lean-Workbook Plus 28301: Trigonometric identity

Proved

WorkbookRestored.plus_28301

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For every real $\theta$ , $\cos\theta+\cos(\theta+2\pi/3)+\cos(\theta+4\pi/3)=0$ .

Source: Lean-Workbook row lean_workbook_plus_28301 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_28301 (θ : ℝ) : Real.cos θ + Real.cos (θ + (2 * Real.pi / 3)) + Real.cos (θ + (4 * Real.pi / 3)) = 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_28301; immutable original Prove2Me node b41a2f33-6bd1-4b9d-8c81-e4ce41d6f657

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