Checking if estimator $\hat{\theta}=\frac{1}{n}\sum_{i=1}^{n}X_{i}^{2}$ is unbiased

Question

Let $P_\theta(X=x) = \left(\frac{\theta}{2}\right)^2(1-\theta)^{1-x^2}$ for $x=-1,0,1$

Let $\hat{\theta}=\frac{1}{n}\sum_{i=1}^{n}X_{i}^{2}$ be an estimator of $\theta$. Is it unbiased?

So the formula that is needed to check if it is biased or not: $$Bias\left(\hat{\theta}\right) = E\left(\hat{\theta}\right) - \theta = 0$$

But I don't really know how to get the expected value here.

$$E\left(\hat{\theta}\right) = E\left(\frac{1}{n}\sum_{i=1}^{n}X_{i}^{2}\right) = \frac{1}{n}E\left(\sum_{i=1}^{n}X_{i}^{2}\right)$$

And I am somehow lost now. What should be my next steps? How to deal with the summation?