# Long trigo

**Geometry**Level 4

\[8\sin\left(\dfrac{x}{4}\right){\cos}^5\left(\dfrac{x}{4}\right) + 8{\sin}^5\left(\dfrac{x}{4}\right)\cos\left(\dfrac{x}{4}\right) - 32{\sin}^3\left(\dfrac{x}{4}\right){\cos}^5\left(\dfrac{x}{4}\right) + 32{\sin}^5\left(\dfrac{x}{4}\right){\cos}^3\left(\dfrac{x}{4}\right) - 16{\sin}^3\left(\dfrac{x}{4}\right){\cos}^3\left(\dfrac{x}{4}\right)\]

Find the value of the above expression at \(x = {30}^\circ\). Scroll right to see the full expression if necessary. Give your answer to 3 decimal places.