Ren's trigonometric equation

Algebra Level 4

Find the sum of all possible values of \(\theta\) (in degrees) restricted to the domain \(0 \leq \theta \leq 360^\circ\), satisfying

\[ \sin^4 \theta + \sin^2 \theta \; \cos^2\theta +\cos ^4 \theta = \frac {3}{4},\]

This problem is posed by Ren Y.

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