Entangled or Not 2

\[|\Psi\rangle = \frac{1}{\sqrt{5}}|\uparrow\uparrow\rangle +\frac{\sqrt{2}}{\sqrt{5}} |\downarrow\uparrow\rangle - \frac{\sqrt{2}}{\sqrt{5}} |\downarrow\downarrow\rangle\]

Is the state \(|\Psi\rangle\) above entangled?

Note: The notation \(|\uparrow\downarrow\rangle = |\uparrow\rangle \otimes |\downarrow\rangle\) is a common shorthand for tensor products of spin states.

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