We know that cosecant theta is hypotenus over opposite of a triangle. We are given that this value is equal to (√17)/4 so 4 is the opposite side of theta. Cotangent theta is the adjacent over opposite. We use the pythagorean theorem to find for the adjacent side.
a = √17 - 4^2
a = 1
Therefore, cotangent of theta is equal to 1/4.