I am having a problem in finding the fundamental period of the given question. I am attaching my method in picture.

I am having a problem in finding the fundamental period of the signal $x(t)$ given below: \begin{align} x(t) &= 2\cos\left(\frac 45 \pi t\right)\sin^2\left(\frac{16}{3} t\right)\\ &= 2\cos\left(\frac 45 \pi t\right)\cdot \frac 12\left[1-\cos\left(\frac{32}{3}t\right)\right]\\ &= \cos\left(\frac 45 \pi t\right) - \cos\left(\frac 45 \pi t\right)\cos\left(\frac{32}{3} t\right)\\ & = \cos\left(\frac 45 \pi t\right)-\frac 12\bigg\{\cos\left[\left(\frac 45 \pi -\frac{32}{3}\right)t\right]+\cos\left[\left(\frac 45 \pi -\frac{32}{3}\right)t\right]\bigg\} \end{align}