Let a vertical tower \( AB \) of height \( 2h \) stands on a horizontal ground. Let from a point \( P \) on the ground a man can see upto height \( h \) of the tower with an angle of elevation \( 2\alpha \). When from \( P \), he moves a distance \( d \) in the direction of \( \overrightarrow{AP} \), he can see the top \( B \) of the tower with an angle of elevation \( \alpha \). If \( d = \sqrt{7}\,h \), then \( \tan \alpha \) is equal to:
