Knowing the Bounding box corner points (circled in red) and the rotation angle, is it possible to find the other point coordinates circled in blue?
I assume there is a tilted rectangle in the figure. If so, then the answer is to your question is yes, it is possible.
I assume you want to know how?
(You should write more specifically.)
Here is one way. Refer to my attachment.
L and H are known, from the coordinates circled in red.
We have similar triangles.
$\displaystyle \frac{w}{z} = \frac{y}{x}$
Also,
$\displaystyle x+w=L$
$\displaystyle y+z=H$
Substitute
$\displaystyle \frac{L-x}{H-y} = \frac{y}{x}$
$\displaystyle x^2-y^2-Lx+Hy=0$
We know that
$\displaystyle \tan 25^\circ=\frac{y}{x}$
We can now solve for $\displaystyle x$ (discard the value $\displaystyle x=0$). From this we can obtain the values of all variables.
When L = 7.5 and H = 8.5, I get $\displaystyle x \approx 4.51901$.