feat(Analysis): strengthen bounds for sin

[b-mehta]

This PR strengthens various bounds for Real.sin in mathlib.
The statement Complex.sin_bound now has a quintic right hand side with a smaller constant. This bound is always better in the range where the theorem applies. The same is true for Real.sin_bound.
Since these changes broke the proof of sin_pos_of_pos_of_le_one, I fixed and golfed this proof.

Next sin_gt_sub_cube is given a tight constant, and its range of validity is extended, and the proof is the same length. A version for weak inequality, and a version with absolute value is also added.

[github-actions]

PR summary 7b507bb714

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ abs_sub_sin_le
+ sin_ge_sub_cube
-+-+ sin_bound

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 7b507bb).

• +2 new declarations
• −0 removed declarations

+Real.abs_sub_sin_le
+Real.sin_ge_sub_cube

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 7b507bb714
Reference commit ba1e3bb0bf

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).