Solve for $θ \in [0, 2 π]$ : $4 sin^{2} θ + 8 cos θ - 7 = 0$ .

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Express $3 cos θ - 4 sin θ$ in the form $R cos (θ + α)$ , where $R > 0$ and $0^{\circ} < α < 9 0^{\circ}$ .
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