This is an offspring of [this](https://mathematica.stackexchange.com/questions/206994/how-to-plot-a-complicated-region) question.

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How to get a nice, smooth, uniform plot of the following? I.e. with no horizontal lines, and no ragged boundary at the top. I went with `PlotPoints` up to `400` and I'm dissapointed. What I'm actually after is a nicely `Export`ed .pdf.

```
ParametricPlot[{{1 + a1/(-1 + a2), 
    1 - 2 ArcCsc[2/Sqrt[1 + a1 - a2]]/π}, 
   a2 >= -1 && 1 + a1 >= a2 && a1 + a2 <= 1}, {a1, -2, 2}, {a2, -1, 
   1}, Frame -> True, PlotRange -> {{0, 2}, {0, 1}}, 
  AspectRatio -> 1/GoldenRatio, PlotPoints -> 150] // Quiet

```

[![enter image description here](https://i.stack.imgur.com/tUc7t.png)](https://i.stack.imgur.com/tUc7t.png)