To write the sine function in terms of cotangent, follow these steps:

Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left.

Replace cosine with its reciprocal function.

Solve the Pythagorean identity tan^{2}θ + 1 = sec^{2}θ for secant.

Replace the secant in the sine equation.

Replace all the tangents with 1 over the reciprocal for tangent (which is cotangent) and simplify the expression.
The result is a complex fraction — it has fractions in both the numerator and denominator — so it’ll look a lot better if you simplify it.

Rewrite the part under the radical as a single fraction and simplify it by taking the square root of each part.

Multiply the numerator by the reciprocal of the denominator.
Voilà — you have sine in terms of cotangent.