I came across Bott's formula in "Vector bundles on complex projective spaces" by Okonek, Schneider & Spindler.
The formula is a formula for $h^q(\mathbb P^n,\Omega^p(k))$, where $\Omega^p(k)$ is the $k$-twisted sheaf of sections in the p-th power of the cotangent bundle of $\mathbb P^n$.
Is there a duality I can use for deriving the value of, say $h^0(\mathbb P^3,\bigwedge^2 T_{\mathbb P^3})$?