Solve `(2^(x)-1)(3^(x)-9)(sinx-cosx)(5^(x)-1)lt0, -pi//2 lt x lt 2pi`.

Explanation

To solve the inequality \((2^{x} - 1)(3^{x} - 9)(\sin x - \cos x)(5^{x} - 1) < 0\) for the interval \(-\frac{\pi}{2} < x < 2\pi\), we will follow these steps:

### Step 1: Identify the critical points
We need to find the values of \(x\) where each factor in the inequality equals zero.

1. **For \(2^{x} - 1 = 0\):**
\[
2^{x} = 1 \implies x = 0
...