The $\sec \theta$ in the denominator is equivalent to $\frac{1}{\cos \theta}$ and $\sin^2 \theta$ in the numerator can be written as $(1-\cos^2 \theta)$. So, the differential equation becomes:
$$\frac { d y } { d \theta } = \frac { e ^ { y } (1-\cos^2 \theta) } {
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