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We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient $\mu(z)$ has the norm $\|\mu\|_\infty=1.$ We employ the pointwise angular dilatation coefficients and this leads to sufficient conditions on $\mu$ which imply the existence of a self-homeomorphism of $\sphere$ satisfying the Beltrami equation with $\mu.$ We also consider the uniqueness of solutions.
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