Trig

cot^-1(-sqrt(11))

$\begin{array}{rcll} x &=& \cot^{-1}{(-\sqrt{11})} \qquad | \qquad \cot{()}\\ \cot{(x)} &=& -\sqrt{11} \qquad | \qquad \cot{(x)} = \frac{1}{\tan{(x)}} \\ \frac{1}{\tan{(x)}} &=& -\sqrt{11} \\ \tan{(x)} &=& \frac{1}{ -\sqrt{11} } \qquad | \qquad \arctan{()}\\ x &=& \arctan{(\frac{1}{ -\sqrt{11} })} \\ \cot^{-1}{(-\sqrt{11})} &=& \arctan{(\frac{1}{ -\sqrt{11} })} \\ &=& \arctan{(\frac{1}{ -3.31662479036 })} \\ &=& \arctan{(-0.30151134458 )} \\ &=& -16.7786548810^{\circ} \end{array}$

heureka has given the angle in the fourth quadrant.  There is also an angle in the second quadrant that satisfies the condition; namely 163.221°

.