If the cosine of the angle between the two circles $x^2+y^2+2 x+4 y-3=0$ and $x^2+y^2+2 k x-2 y-1=0$ is $\frac{1}{2 \sqrt{3}}$ then $k^2=$

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If the cosine of the angle between the two circles $x^2+y^2+2 x+4 y-3=0$ and $x^2+y^2+2 k x-2 y-1=0$ is…