Exercise description for "Prepare Arbitrary State" incorrectly constrains α as non-negative

[minestarks]

In the Single-Qubit Gates kata, the "Prepare Arbitrary State" exercise description states:

1. A non-negative real number α.
2. A non-negative real number β = √(1 − α²).

However, the verification test generates test cases with negative α values (e.g., alpha = Cos(2) ≈ -0.416), and the reference solution uses ArcTan2(beta, alpha) which handles negative α correctly.

Why the "non-negative" constraint is wrong

The pedagogical goal of this exercise is to teach students to use ArcTan2(beta, alpha) rather than the simpler ArcSin(beta). If α were truly non-negative, a student could ignore the alpha parameter entirely and write:

Ry(2.0 * ArcSin(beta), q);
R1(theta, q);

This would trivially pass, defeating the purpose of the exercise. The exercise hint even explicitly mentions ArcTan2, confirming the intended solution requires both inputs.