Can someone check if this “proof” is correct?

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I posted about this a few weeks ago, but I am trying to determine if there is some point south of Seattle (along the same longitude) in the continental United States with a larger geodesic distance from Fort Lauderdale. The problem is written more formally in terms of spherical coordinates. Using a formula for geodesic distance I found online (images shown), I used Desmos to plot the geodesic distance as a function of the longitude of the point near Seattle. The distance seems to oscillate when this angle is varied, but can someone check this for accuracy?

Problem setup and assumptions

Desmos setup

Desmos graph

First formula from source

Final formula from source

Source

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