I want to evaluate the following expectation. $$\mathbb{E}_{U\text{~Haar}} ||I-U||$$ where $||\cdot||$ is the operator norm (i.e., the maximum eigenvalue.). This is equivalent to the integral of
$$ \frac{1}{n!(2\pi)^n}\max_i|1-e^{i\theta_i}|\prod_{j\le k}|e^{i\theta_j}-e^{i\theta_k}|^2 $$ over $(\theta_i,...,\theta_n)\in[0,2\pi]^{\times n}$. How do I calculate this integral?