Solve a Trigonometric Equation!

Geometry Level 4

\[ \large 2^{1+3\cos x} - 10 \cdot 2^{-1+2\cos x} + 2^{2+\cos x} - 1 = 0 \]

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

Give your answer to 2 decimal places.

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