For example, when solving the equation $$\sin(13x)+\sin(9x)=\cos(2x)$$ (by hand) you get the solutions $$ x= \begin{cases} \pm\tfrac{\pi}{4}+\pi n,\\ \tfrac{\pi}{66}+\tfrac{2}{11}\pi n,\\ \tfrac{5\pi}{66}+\tfrac{2}{11}\pi n, \end{cases} \qquad n\in\mathbb{Z}. $$

I can make a graphic illustration of the solutions with the following (primitive) code;

```
Clear[x1, x2, x3, x4, n]
x1[n_] := \[Pi]/66 + 2/11 \[Pi] n
x2[n_] := 5 \[Pi]/66 + 2/11 \[Pi] n
x3[n_] := -\[Pi]/4 + \[Pi] n
x4[n_] := \[Pi]/4 + \[Pi] n
p1 = Table[{Cos[x1[n]], Sin[x1[n]]}, {n, 0, 10}];
p2 = Table[{Cos[x2[n]], Sin[x2[n]]}, {n, 0, 10}];
p3 = Table[{Cos[x3[n]], Sin[x3[n]]}, {n, 0, 1}];
p4 = Table[{Cos[x4[n]], Sin[x4[n]]}, {n, 0, 1}];
Graphics[{Circle[{0, 0}, 1], Point[p1], Point[p2], Point[p3], Point[p4]}]
```

but is there a smarter/more efficient way to make the plot (and perhaps with a little more ‘fancy’ output)? TIA.