3. Find the rational number - the value of the expression

$$
\cos ^{6}(3 \pi / 16)+\cos ^{6}(11 \pi / 16)+3 \sqrt{2} / 16
$$
Solution: By the reduction formula, the desired expression is equal to $\sin ^{6}(5 \pi / 16)+\cos ^{6}(5 \pi / 16)+3 \sqrt{2} / 16$. By the sum of cubes formula, we have: $\cos ^{6}(5 \pi / 16)+\sin ^{6}(5 \pi / 16)=1-\frac{3 \sin ^{2}(10 \pi / 16)}{4}$. Therefore, our expression takes the form: $1-\frac{3 \sin ^{2}(10 \pi / 16)}{4}+\frac{3 \sqrt{2}}{16}=1-\frac{3}{4}\left(\frac{1-\cos (5 \pi / 4)}{2}\right)+\frac{3 \sqrt{2}}{16}=\frac{5}{8}$. Answer: $5 / 8$.