If the angle between the line \( x= \frac{y-4}{2}=\frac{z-1}{\lambda} \) and the plane \( x + 3y + z = 1 \) is \( \cos ^{ -1 }{ \left( \sqrt { \frac { 10 }{ 11 } } \right) }, \) what is \( \lambda?\)

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Let \(\alpha,\beta,\) and \(\gamma\) be the angles that the line \(\frac{x-2}{3}=-\frac{y+1}{4}=\frac{z+3}{5}\) forms with the \(xy\)-, \(yz\)-, and \(xz\)-planes. Then what is the value of \(\sin^2\alpha+\sin^2\beta+\sin^2\gamma?\)

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