Let

Solve the equation

If you take $\tan$ of both sides first, you have

and you can use implicit differentiation to find

If your expression for $\frac{dy}{dx}$ contains a ${\sec }^2(y)$, remember that

and notice that

so you can give $\frac{dy}{dx}$ in terms of $x$ only!

Once you have an expression for $\frac{dy}{dx}$ in terms of $x$ only, you can find $\frac{d^{2}y}{d{x}^2}$ without using implicit differentiation - you just need the chain (or quotient) rule.

Let the roots be $\alpha ,\beta \in \mathbb{Q}$.

give the value of