Solve the SDE:
$$ dX = \cos(X)\sin^3(X)dt +\sin^2(X)dW $$
where $W$ is a Brownian motion. The SDE has initial condition $X(0) = \frac{\pi}{2}$. I am given the hint that $\int dx/\sin^2(x) = -\cot(x) + C$.
My idea is to use Ito's formula - however I have no idea which function to try this with.
Hint 1. Let's use Ito's lemma for $f(t,X) = \cot(X)$.
Hint 2. It will give us: $\underbrace{[\ldots]}_{\star} dt + [\ldots]dW_t$. What will happen with $\star$.