feat: cotangent q-expansion

[CBirkbeck]

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Add the q-expansion of the cotangent function that will be needed for Eisenstein series q-expansions.

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• [x] depends on: #12758
• [x] depends on: #12771

[mergify[bot]]

⚠️ The sha of the head commit of this PR conflicts with #12758. Mergify cannot evaluate rules on this PR. ⚠️

[leanprover-community-mathlib4-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#12758~~
• ~~leanprover-community/mathlib4#12771~~ By Dependent Issues (🤖). Happy coding!

[github-actions[bot]]

PR summary 8dfef7341d

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Analysis.Complex.UpperHalfPlane.Exp	1436
Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent	1437

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Declarations diff

+ Complex.cot_eq_exp_ratio + Complex.cot_pi_eq_exp_ratio + UpperHalfPlane.abs_exp_two_pi_I_lt_one + pi_mul_cot_pi_q_exp

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>

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde.

[mathlib-bors[bot]]

:v: CBirkbeck can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[CBirkbeck]

bors r+

[mathlib-bors[bot]]

Pull request successfully merged into master.

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