Remark
The 68° will get you 1/2 the base if you use the right trig function.
After that, all you need do is use the Cone Formula for Volume.
Step One
Find 1/2 the base.
The height and 1/2 the base are in a right triangle. Put into more formal language
Tan(68°) = Opposite side / Adjacent Side
Givens
Angle = 68°
Opposite Side = 4.2 feet.
Substitute
Adjacent side = opposite Side / Tan(68°)
Adjacent side = 4.2 / Tan(68°)
Adjacent side = 1.697 feet
Step Two
Find the Volume
Formula
V = 1/3 pi r^2 h
Givens
V = ???
pi = 3.14
r = 1.6969
h = 4.2 feet.
Solve
V = 1/3 3.14 * 1.6969^2 * 4.2
V = 12.66 cubic feet.