#### Answer

Concave upwards for all $\theta$ in (0,$\pi$) and
concave down for all $\theta$ in ($\pi, 2\pi$). The point of inflection is at $\theta=\pi$.

#### Work Step by Step

$y=f(\theta)=\theta-2\sin \theta$
$f'(\theta)=1-2\cos\theta$
$f''(\theta)=-2\times-\sin\theta=2\sin\theta$
$f''(\theta)$ is positive when $\theta\in(0,\pi)$ and is negative when $\theta\in (\pi,2\pi)$.