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To compute this sum, we can use a nifty algebraic approach:

Let S be the sum, so:

S = 3 + 6 + 9 + 12 + ... + 996 + 999

We can also write S as:

S = 999 + 996 + ... + 12 + 9 + 6 + 3

Adding these two equations together we get:

2S = 1002 + 1002 + ... + 1002 + 1002

Where there are 333 1002's in the above equation.

This leads us to:

2S = 1002 * 333

S = 501 * 333 = 166,833.

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