`2sin^2(pi/6 )+c o s e c^2((7pi)/6)cos^2(pi/3)=3/2`

Explanation

To solve the equation \( 2\sin^2\left(\frac{\pi}{6}\right) + \csc^2\left(\frac{7\pi}{6}\right) \cos^2\left(\frac{\pi}{3}\right) = \frac{3}{2} \), we will follow these steps:

### Step 1: Convert to sine and cosine
We start with the left-hand side of the equation:
\[ 2\sin^2\left(\frac{\pi}{6}\right) + \csc^2\left(\frac{7\pi}{6}\right) \cos^2\left(\frac{\pi}{3}\right) \]

...