${sin}^{2} x (1 + tan x) = 3 sin x (cos x - sin x) + 3$

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Solution

${sin}^{2} x (1 + tan x) = 3 sin x cos x + 3 {cos}^{2} x$
Divide throughput by ${cos}^{2} x (cos x \neq 0)$ and put $tan x = t$
$t^{2} (1 + t) = 3 (t + 1)$
or $t + 1 = 0$ or $t^{2} = 3$
$∴ tan x = - 1$ or $\pm \sqrt{3}$
$∴ x = n π - \frac{π}{4}$ or $n π \pm \frac{π}{3}$ .

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