For the rotation minus, start fraction, 21, pi, divided by, 4, end fraction− 421π​ , 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 is between 0 and 2π.

Given angle is -21π/4.

Step 1: Add 2π to the given angle until it falls within the desired range. Since 2π is equivalent to 8π/4, we can add this to our angle.

-21π/4 + 8π/4 = -13π/4

This is still less than 0, so we add 2π again.

-13π/4 + 8π/4 = -5π/4

Still less than 0, so add 2π once more.

-5π/4 + 8π/4 = 3π/4

Now, our angle is between 0 and 2π, so 3π/4 is the coterminal angle.

Step 2: Determine the quadrant.

The angle 3π/4 lies in the second quadrant because it is between π/2 and π.

Step 3: Find the reference angle.

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

So, the reference angle is π - 3π/4 = π/4.

So, the coterminal angle is 3π/4, it lies in the second quadrant, and the reference angle is π/4.