Solve a Trigonometric Equation!

Geometry Level 4

21+3cosx1021+2cosx+22+cosx1=0 \large 2^{1+3\cos x} - 10 \cdot 2^{-1+2\cos x} + 2^{2+\cos x} - 1 = 0

If xx in the interval 0x<2π0 \leq x < 2 \pi , find the sum of all possible values of xx satisfying the equation above.

Give your answer to 2 decimal places.

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