Find the length of the curve $\mathcal C$, $x(t)=2\cos^3(t)$, $y(t)=2\sin^3(t)$ for $0 ≤ t ≤ 2π$.

I got a bit stuck trying to do this. I started off by finding $dx/dt$ and $dy/dt$ ($-6\cos^2(t)\sin(t)$ and $6\sin^2(t)\cos(t)$ respectively). Then, I found the modulus for this which I found to be $6\sin t\cos t$. 

Then, I integrated by substituting $u=\sin t$ and got $\sin t$. However, I am unsure which limits to chose as if I use $2π$ and $0$, then the answer returned is $0$, which I am pretty sure is not the answer. Any help on how to choose the limits would be appreciated, or pointing out if I've made any mistakes.