For $\mathrm{p}>0$, a vector $\overrightarrow{\mathrm{v}}_2=2 \hat{\mathrm{i}}+(\mathrm{p}+1) \hat{\mathrm{j}}$ is obtained by rotating the vector $\overrightarrow{\mathrm{v}}_1=\sqrt{3} p \hat{\mathrm{i}}+\hat{\mathrm{j}}$ by an angle $\theta$ about origin in counter clockwise direction. If $\tan \theta=\frac{(\alpha \sqrt{3}-2)}{(4 \sqrt{3}+3)}$, then the value of $\alpha$ is equal to $\_\_\_\_$ .