Ren's trigonometric equation

Algebra Level 4

Find the sum of all possible values of θ\theta (in degrees) restricted to the domain 0θ3600 \leq \theta \leq 360^\circ, satisfying

sin4θ+sin2θ  cos2θ+cos4θ=34, \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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