Ellipse described with little information

Geometry Level pending

Let \(S\) be the focus of an ellipse.Let the latus rectum of the ellipse through \(S\) intersect the ellipse at \(P\) and \(Q\).Tangents to the ellipse at points \(P\) and \(Q\) intersect at a point \(R\).

Given that \(\angle QRP = 60^\circ\) , find the eccentricity of the ellipse.

Submit your answer to three decimal places.

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