3. Using the method of auxiliary argument, we arrive at the equation

$$
\sqrt{\sin ^{4} b+\cos ^{4} b} \cos (x-\varphi(b))=a
$$

The answer to the problem will be $a$ satisfying the relation

$$
|a|>\min _{b} \sqrt{\sin ^{4} b+\cos ^{4} b}=\min _{b} \sqrt{1-\frac{1}{2} \sin ^{2} 2 b}=\frac{1}{\sqrt{2}}
$$
Answer: $a \in(-\infty,-1 / \sqrt{2}) \cup(1 / \sqrt{2},+\infty)$.

Remark: It is implied that the equation may have no solutions at all for any $b$. Answer to the variant: $2-2: a \in(-\infty, 1-\sqrt{2}) \cup(\sqrt{2}-1,+\infty)$.