Does the inequality $\Bbb E \left[ \frac{1}{\tan(x)} \right] \leq \frac{1}{\tan(\Bbb E[x])}$ hold?

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Given a random variable $x$ and expectation $\Bbb E$, does the following inequality hold?

$$\Bbb E \left[ \frac{1}{\tan(x)} \right] \leq \frac{1}{\tan(\Bbb E[x])}$$