Paragraph: Let a, b, c, d ∈ R . Then the cubic equation of the type...

Paragraph: Let $a, b, c, d \in R$. Then the cubic equation of the type $a x^3+b x^2+c x+d=0$ has either one root real or all three roots are real. But in case of trigonometric equations of the type $a \sin ^3 x+b \sin ^2 x+c \sin x+d=0$ can possess several solutions depending upon the domain of $x$. To solve an equation of the type $a \cos \theta+b \sin \theta=c$. The equation can be written as $\cos (\theta-\alpha)=c / \sqrt{\left(a^2+b^2\right)}$. The solution is $\theta=2 \mathrm{n} \pi+\alpha \pm \beta$, where tan $\alpha=b / a, \cos\beta=c / \sqrt{\left(a^2+b^2\right)}$Question: In the interval $[-\pi / 4, \pi / 2]$, the equation, $\cos 4 x+\frac{10 \tan x}{1+\tan ^2 x}=3$ has