If a unit vector \(\vec a\;{\rm{makes\;angles\;}}\frac{\pi }{3}\;{\rm{with}}\;\hat i,\frac{\pi }{4}\;{\rm{with}}\;\hat j\) and θ ϵ (0, π) with , then the value of θ is:

• A. \(\frac{{5\pi }}{6}\)
• B. π/4
• C. \(\frac{{5\pi }}{{12}}\)
• D. \(\frac{{2\pi }}{3}\)