What are the minimum and maximum values for this function?

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I have to draw the graph of the flat curve

$$ x = \frac{a}{4*\cos^2(t) -3} \\ y= \frac{a* \tan t}{4*\cos^2(t) -3} \\ \text{where } \ \ a =0.2 ,\ t \in \ (-\pi/2, \pi/2) \ \backslash \{-\pi/6, \pi/6\} $$

I search on the internet more information about this curve but I did not find anything. For $x$ I think the minimum value is $\frac{0.2}{-3}$ since the cosine function is $0$ for $-\pi/2 $. The curve's name is trisectrix of Longchamps. Thank You!

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Polar coordinates : $$\begin{cases} x=\rho\cos(t)=\frac{a}{4\cos^2(t) -3}=\frac{a}{\cos(3t)}\cos(t)\\ y=\rho\sin(t)=\frac{a \tan t}{4*\cos^2(t) -3}=\frac{a}{\cos(3t)}\sin(t) \end{cases} \quad\implies\quad \rho=\frac{a}{\cos(3t)}$$

because $\cos(3t)=\cos(t)(4\cos^2(t) -3)$

This is the equation of the "equilateral trifoil" or "Longchamps trisectrix".

For properties see: https://www.mathcurve.com/courbes2d.gb/trefleequilatere/trefleequilatere.shtml