Trigonometric equation: $2(\sin^6 x+\cos^6 x)-3(\sin^4 x+\cos^4 x)+1=0$ I'm new here, but I need your help so much to solve an equation:
$$2(\sin^6 x+\cos^6 x)-3(\sin^4 x+\cos^4 x)+1=0$$
I tried a lot like making $2[(\sin^2 x)^3 + (\cos^2 x)^3$

Hint: $x^6 + y^6 = (x^2 + y^2)(x^4 - x^2y^2 + y^4)$. Then look for squares.
Also, it is not equal to zero, but to $-1$.
