The cosine function, (x), has a range of values between -1 and 1, inclusive. This means that for any real angle x, we must have:

The cosine function, $\cos(x)$, has a range of values between -1 and 1, inclusive. This means that for any real angle $x$, we must have:

The equation given is $\cos(2\theta + 120^\circ) = \frac{3}{2}$.
The value $\frac{3}{2}$ is equal to 1.5.

Since $1.5 > 1$, the value $\frac{3}{2}$ falls outside the possible range of the cosine function.
Therefore, there is no real angle $x$ for which $\cos(x) = 1.5$.

Conclusion:
There are no solutions for $\theta$ that satisfy the given equation.

The final answer is $\text{No solution}$.