Triangulating Angles
JavaScript (ES6), 76 bytes
Expects the angles in radians. Returns either [x,y] or 0 if the lines are parallel or coincident.

(x,y,a,X,Y,A)=&gt;a-A&amp;&amp;[(m=(t=Math.tan)(a))*(X-=(x-=m*y)+t(A)*Y,X/=m-t(A))+x,X]

Try it online!
Or 71 bytes if we can just return [Infinity,Infinity] for invalid inputs.