number theory - What is the remainder when 4 to the power 1000 is divided by 7

What is the remainder when $4^{1000}$ is divided by 7?
In my book the problem is solved, but I am unable to understand the approach. Please help me understand -

Solution -

To find the Cyclicity, we keep finding the remainders until any
remainder repeats itself. It can be understood with the following
example:

No./7 -> $4^1$ $4^2$ $4^3$ $4^4$ $4^5$ $4^6$ $4^7$ $4^8$

Remainder -> 4 2 1 4 2 1 4 2

Now $4^4$ gives us the same remainder as $4^1$, so the Cyclicity is of
3 (Because remainders start repeating themselves after $4^3$

So any power of 3 or multiple of 3 will give the remainder of 1. So,
$4^{999}$ will give remainder 1.

Final remainder is 4.

Now I don't understand the last line. Please explain, how the remainder comes down to 4?