Can you find the angle value?

$\triangle CDE$ is equilateral so the angle at $D$ is $60^{\circ}$ . This is a central angle at $D$ but an inscribed angle at $C$ , so $\angle C=30^{\circ}$ .

Do it again on the other circle where now $C$ is a central angle but $A$ is an inscribed angle. $\angle A = \boxed{15^{\circ}}$

Since $\triangle CDE$ is equilateral, $\angle DCE=60^{\circ}$ . And as $\overline{EF}$ is diameter, $\angle ECF=90^{\circ}$ . $\Rightarrow \angle DCF=30^{\circ} \Rightarrow \angle CAF=15^{\circ}$