What If I take $$a^2+b^2+c^2=11$$ out

Geometry Level pending

Consider triangle $$ABC$$, such that:

1. $$\angle A = 45^\circ$$

2. $$\tan A, \tan B, \tan C$$ are in an arithmetic progression.

Find $$\dfrac{{CH}^2}{\triangle}$$ to 4 decimal places, where $$H$$ is the orthocenter and $$\triangle$$ is the area of triangle $$ABC$$.

Inspiration

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