3.074. $\sin ^{2}(\alpha+2 \beta)+\sin ^{2}(\alpha-2 \beta)-1$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

3.074. $\sin ^{2}(\alpha+2 \beta)+\sin ^{2}(\alpha-2 \beta)-1$.
Solution.

$$
\sin ^{2}(\alpha+2 \beta)+\sin ^{2}(\alpha-2 \beta)-1=\frac{1-\cos (2 \alpha+4 \beta)}{2}+
$$

$+\frac{1-\cos (2 \alpha-4 \beta)}{2}-1=\frac{1}{2}-\frac{\cos (2 \alpha+4 \beta)}{2}+\frac{1}{2}-\frac{\cos (2 \alpha-4 \beta)}{2}-1=$ $=-\frac{1}{2}(\cos (2 \alpha+4 \beta)+\cos (2 \alpha-4 \beta))=-\frac{1}{2} \cdot 2 \cos 2 \alpha \cos 4 \beta=-\cos 2 \alpha \cos 4 \beta$.

Answer: $-\cos 2 \alpha \cos 4 \beta$.