Is there a way to simplify this trig expression without a calculator?

Question

Solved this using a calculator, but wanted to know if it can be done, at least partially, by hand. Not looking for all solutions of x (unless there's a general formula). Just the lowest, positive x value this equation is true

sec(pi*x/4)tan(pi*x/4) = [sqrt(2)-4]x + 4

Answer 1

sec(pi*x/4)tan(pi*x/4) = [sqrt(2)-4]x + 4

sec(π/4)tan(π/4)=[(√2)-4]x+4

sec(π/4)=√2

tan(π/4)=1

have x=[(√2)-4]/[(√2)-4}=1

Answer 2

The secant is the reciprocal of the cosine function (1/cos). The tangent is equal to the sine function divided by the cosine function.

So sec × tan = sin / cos² = sin ( x ) / [ 1 - sin( x² ) ].

I would start here. When I have more time, I will get back to this. The bat phone just rang!