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## Homework Statement

Show that the equation below connects the point [tex](r_{0}, \theta_{0})[/tex] to the point [tex](r_{1}, \theta_{1})[/tex], [tex]\theta_{0}\neq\theta_{1}[/tex], along a curve that everywhere forms the same angle with the rays [tex]\theta=constant[/tex].

And here's the equation. I can't get the Latex to work... no clue why.

## Homework Equations

N/A.

## The Attempt at a Solution

This is part of a larger problem on stereographic projection - I've figured out that this equation, if projected onto a sphere, traces out a loxodrome. I also know that I essentially have to prove that that mess of an equation is a equiangular spiral (logarithmic spiral).

The problem is, no matter how I look at it, I need to calculate the derivative [tex]dr/d\theta[/tex], which - from where I'm looking - looks like one hell of a messy and convoluted derivative, which I'd rather not do.

Is there an easier, cleaner, more elegant way of solving this problem than brute-forcing the derivative? If not, how do I do the derivative?