Find the number of roots of the equation `16sec^3theta-12tan^2theta-4sectheta=9` in interval `(-pi,pi)`

Explanation

To solve the equation \( 16 \sec^3 \theta - 12 \tan^2 \theta - 4 \sec \theta = 9 \) in the interval \( (-\pi, \pi) \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ 16 \sec^3 \theta - 12 \tan^2 \theta - 4 \sec \theta - 9 = 0 \]
Since we have both \(\sec\) and \(\tan\), we can express \(\tan^2 \theta\) in terms of \(\sec\):
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