Angles in pyramid 
We have to find the value of $\cos\theta$.
I tried it alot. But could not able to do it.
Solution given in the book

HINTS:
Shall be brief, hope you fill in details.
Let $AB= 4 b$ then side of inner square on base $ 2 \sqrt 2 b = 2d $ say
Let $OA = h. \, $ Projections on midface and base are $ h \cos \beta, h \sin \beta \,$ where $ 2\beta = AOB$
If $H$ is side of dihedral angle $ 2 \gamma$ between slant faces  
$$ \dfrac{1}{H^2}=\dfrac{1}{(h \cos \beta)^2}+ \dfrac{1}{(h \sin \beta)^2} $$
$$ \sin \gamma= \frac{d}{H} $$
