Zsolt,

Thank you.  That's it.  Thanks again.

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Try working with 1/A. 

You can use the CriticalPoints and the Roots commands of the Student package to solve your problem.

Try this:

restart;
with(plots):with(Student[Calculus1]):
a := 2; b := 1;
A := (a*b)^2/(8*cos(theta)*sin(theta)*(a*sin(theta)+b*cos(theta))^2);
Agraph:=plot(A,theta=-2..5,view=[-2..5,-15..15],numpoints=3000,color=red):
Ad:=diff(A,theta);
Adgraph:=plot(Ad,theta=-5..10,view=[-2..5,-15..15],numpoints=3000,color=blue):
cpoints:=CriticalPoints( A,theta=-2..5 );
rpoints:=Roots( Ad,theta=-2..5,numeric);
Adisconts:=pointplot(zip((x,y)->[x,y],cpoints, [],0),color=blue,symbol=circle):
Adzeros:=pointplot(zip((x,y)->[x,y],rpoints, [],0),color=green,symbol=circle):
display(Agraph,Adgraph,Adisconts,Adzeros);