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 $2[(\sin^2 x)^3 + (\cos^2 x)^3$

$$2(\sin^6 x+\cos^6 x)-3(\sin^4 x+\cos^4 x)=0$$
$\sin x=t,\cos^2x=1-t^2$
$$2(t^6+(1-t^2)^3)-3(t^4+(1-t^2)^2)=0$$
$$2(t^6+1-3t^2+3t^4-t^6)-3(t^4+1-2t^2+t^4)=0$$
$$2(1-3t^2+3t^4)-3(2t^4+1-2t^2)=0$$
$$(2-6t^2+6t^4)-(6t^4+3-6t^2)=0$$
$$-1=0$$ CONTRADICTION
