The maximum value of the expression `1/(sin^2 theta + 3 sin theta cos theta + 5cos^2 theta)` is

Explanation

To find the maximum value of the expression \( \frac{1}{\sin^2 \theta + 3 \sin \theta \cos \theta + 5 \cos^2 \theta} \), we will follow these steps:

### Step 1: Identify the Denominator
The expression can be rewritten as:
\[ E = \frac{1}{D} \]
where \( D = \sin^2 \theta + 3 \sin \theta \cos \theta + 5 \cos^2 \theta \).
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