Use an identity to write the expression as a single trigonometric function value or as a single number. \[ \frac{1}{6}-\frac{1}{3} \sin ^{2} 35.9^{\circ} \] \[ \frac{1}{6}-\frac{1}{3} \sin ^{2} 35.9^{\circ}= \] (Type an exact answer, using radicals as needed. Do not include the degree symbol in your answer.)

Step 1 ：Given the expression \(\frac{1}{6}-\frac{1}{3} \sin ^{2} 35.9^{\circ}\)

Step 2 ：We can use the Pythagorean identity in trigonometry, which states that \(\sin^2(x) + \cos^2(x) = 1\). From this identity, we can express \(\sin^2(x)\) as \(1 - \cos^2(x)\).

Step 3 ：Substituting this into the given expression, we get \(\frac{1}{6}-\frac{1}{3} (1 - \cos^2(35.9^{\circ}))\)

Step 4 ：Converting the angle to radians, we get approximately 0.627 radians.

Step 5 ：Calculating the cosine of this angle, we get approximately 0.810.

Step 6 ：Substituting this value back into the expression, we get approximately 0.052.

Step 7 ：Final Answer: The expression \(\frac{1}{6}-\frac{1}{3} \sin ^{2} 35.9^{\circ}\) simplifies to \(\boxed{0.052}\).