#### Zurtex

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[tex]d\left(r^3 (\cos (4 \theta) dr - r \sin (4\theta) d\theta)\right)[/tex]

Simplified:

[tex]d\left(r^3 \cos (4\theta) dr - r^4 \sin (4\theta) d\theta\right)[/tex]

Goes to:

[tex]2r^3 dr \left(-4 \sin (4\theta) d\theta dr - 4r^3 dr \cos (4\theta) d\theta d\theta \right) = 0[/tex]

Am I even slightly right?