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I am trying to find the points where a parametric curve meets itself.

$$x= -\frac{2}{\pi} + \cos t \text{ and } y = -\frac{2t}{\pi} + \sin t, \text{ where } t\in (-\pi, \pi).$$

Asuming $t, s$ are such that the curve meets itsef from $x(t)= x(s)$ I get $t=-s$ substituting in 2, I arrive to $2t = \pi \sin t$.

No there I am stuck, can I get a hint

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    Did you notice that this is the equation of a circle ? – 2017-02-28
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    It's not a circle because of the second t in y(t). – 2017-03-03
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    what about the curve cutting itself at $x = -2/\pi, y = 0$ for $t = \pm \pi/2?$ – 2017-03-03

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