For the rotation minus, start fraction, 21, pi, divided by, 4, find the coterminal angle from 0, is less than or equal to, theta, is less than, 2, pi0≤θ<2π, the quadrant, and the reference angle.

To find the coterminal angle, we need to add or subtract multiples of 2π until we get an angle that falls within the desired range of 0 ≤ θ < 2π.

Given angle is -21π/4.

Step 1: Convert the angle to positive by adding 2π. Since we're dealing with fractions, it's easier to use 8π/4 (which is equal to 2π) instead.

-21π/4 + 8π/4 = -13π/4

This is still negative, so we need to add 2π again.

-13π/4 + 8π/4 = -5π/4

Still negative, so add 2π once more.

-5π/4 + 8π/4 = 3π/4

Now we have a positive angle that falls within the desired range, so 3π/4 is the coterminal angle.

Step 2: Determine the quadrant.

The angle 3π/4 lies in the second quadrant.

Step 3: Find the reference angle.

The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. In the second quadrant, the reference angle is π - θ.

π - 3π/4 = π/4

So, the reference angle is π/4.