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If the equations $x=1+2 \cos \theta, y=2+\sin \theta, 0 \leq \theta < 2 \pi$ represent an ellipse, then the point of intersection of the normal drawn at $\mathrm{P}\left(\frac{\pi}{4}\right)$ to this ellipse and its major axis is
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$\left(\frac{4-\sqrt{3}}{4}, 0\right)$
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