feat(Chebyshev polynomials): Prove that the roots of the Chebyshev polynomials (except 0) are irrational.

[yuanyi-350]

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[github-actions]

PR summary 20b873c44e

Import changes exceeding 2%

%	File
+11.49%	Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema	1924	2145	+221 (+11.49%)
Mathlib.NumberTheory.Niven	1945	1948	+3 (+0.15%)

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.Niven	3
Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema	221

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Declarations diff

+ irrational_cos_chebyshev_angle
+ irrational_of_root_T_real

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[YuvalFilmus]

I have a competing PR #34044.
Not enough of an expert to say which one is better...