The remainder when $(672 + 541 + 383 + 295 + 101 + 86)$ is divided by 3, is:

When finding remainders for division by 3, the remainder of any number divided by 3 equals the remainder when the sum of its digits is divided by 3.

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For 672: $6+7+2 = 15$, which gives remainder $0$ when divided by 3

For 541: $5+4+1 = 10$, which gives remainder $1$ when divided by 3

For 383: $3+8+3 = 14$, which gives remainder $2$ when divided by 3

For 295: $2+9+5 = 16$, which gives remainder $1$ when divided by 3

For 101: $1+0+1 = 2$, which gives remainder $2$ when divided by 3

For 86: $8+6 = 14$, which gives remainder $2$ when divided by 3

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The sum of all remainders:

$0 + 1 + 2 + 1 + 2 + 2 = 8$

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Finding the remainder when 8 is divided by 3:

$8 = 3(2) + 2$

Therefore, the remainder is $2$.