The minimum value of 64 ` sec theta+27 "cosec" theta ` where ` theta in (0,(pi)/(2))` is _________

Explanation

To find the minimum value of the expression \( 64 \sec \theta + 27 \csc \theta \) where \( \theta \) is in the interval \( (0, \frac{\pi}{2}) \), we will follow these steps:

### Step 1: Rewrite the expression in terms of sine and cosine
We can express secant and cosecant in terms of sine and cosine:
\[ \sec \theta = \frac{1}{\cos \theta}, \quad \csc \theta = \frac{1}{\sin \theta} \]
Thus, the expression becomes:
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