The magnitude of vectors → OA , → OB and → OC in the given figure...

From the above diagram, the equations are,
\overset{\to}{OA} = R\left[cos{30}^{∘}\overset{^}{i} + sin{30}^{∘}\overset{^}{j}\right]

\overset{\to}{OB} = R\left[cos{60}^{∘}\overset{^}{i} - \sin 60 ° \overset{^}{j}\right]

\overset{\to}{OC} = R\left[- \cos 45 ° \overset{^}{i} + \sin 45 ° \overset{^}{j}\right]

⇒ \overset{\to}{OA} + \overset{\to}{OB} - \overset{\to}{OC} = R\left[\dfrac{1}{2} + \dfrac{\sqrt{3}}{2} + \dfrac{1}{\sqrt{2}}\right]\overset{^}{i} + R\left[\dfrac{1}{2} - \dfrac{\sqrt{3}}{2} - \dfrac{1}{\sqrt{2}}\right]\overset{^}{j}, angle with the $x -$axis.

$⇒ tan\alpha = \dfrac{\dfrac{1}{2} - \dfrac{\sqrt{3}}{2} - \dfrac{1}{\sqrt{2}}}{\dfrac{1}{2} + \dfrac{\sqrt{3}}{2} + \dfrac{1}{\sqrt{2}}} = \dfrac{1 - \sqrt{3} - \sqrt{2}}{1 + \sqrt{3} + \sqrt{2}}$

$⇒ \alpha = \tan^{- 1}\left[\dfrac{1 - \sqrt{3} - \sqrt{2}}{1 + \sqrt{3} + \sqrt{2}}\right]$.