3. (10 points) Let $[x]$ denote the greatest integer not exceeding $x$, for example $[10.2]=10$. Then $\left[\frac{2017 \times 3}{11}\right]+\left[\frac{2017 \times 4}{11}\right]+\left[\frac{2017 \times 5}{11}\right]+\left[\frac{2017 \times 6}{11}\right]+\left[\frac{2017 \times 7}{11}\right]+\left[\frac{2017 \times 8}{11}\right]$ equals ـ. $\qquad$
【Analysis】This problem examines the Gaussian integer part. Observing the expression, we can see that the sum of the numbers within the brackets of the first two terms equals 2017. Since when $x$ is not an integer, $[x]+[2017-x]=2016$, by adding them in pairs, we can obtain the answer.

【Solution】Since 2017 and 11 are prime numbers, the numbers within the brackets are not integers,
$$
\text{then }\left[\frac{2017 \times 3}{11}\right]+\left[\frac{2017 \times 8}{11}\right]=2017-1=2016 \text{, }
$$

Similarly, $\left[\frac{2017 \times 4}{11}\right]+\left[\frac{2017 \times 7}{11}\right]=2016$,
$$
\left[\frac{2017 \times 5}{11}\right]+\left[\frac{2017 \times 6}{11}\right]=2016 \text{, }
$$

Therefore, the original expression $=2016+2016+2016=6048$.
Hence, the answer is: 6048