The second hand does not represent the radius of the clock. Its length runs along the hypotenuse of the right triangle that runs from the tip of the second hand to the tip of the hour hand, along the hour hand, and then finally along the second hand. The angle $\displaystyle \theta$ does not equal $\displaystyle \dfrac{2}{3}$. An angle of $\displaystyle \dfrac{2}{3}$ is approximately 10% of the circumference of the circle. The angle you want is $\displaystyle \dfrac{2}{3}$ of $\displaystyle \dfrac{\pi}{2}$. In other words, $\displaystyle \theta = \dfrac{\pi}{3}$. And $\displaystyle \cos\left(\dfrac{\pi}{3}\right) = \dfrac{1}{2}$.