A table of special angles

You will build the table of special angles in Python and use it to work out an expression.

Your tasks.

1. In ratios, return a tuple (sin, cos, tan) for an angle in degrees, each rounded to $4$ places. When the cosine is $0$, give None for the tangent.
2. In sine_by_pattern, return $\dfrac{\sqrt{k}}{2}$ for the $k$th special angle: $k = 0$ for $0^\circ$, up to $k = 4$ for $90^\circ$.
3. Set value to $\sin^2 30^\circ + \cos^2 60^\circ + \tan^2 45^\circ$, using ratios.